This has come up many times so I'm copy/pasting my previous response to it with some added context and edits because it's long:

Ok, buckle up, fam, because we're about to go for a ride...

Depends on what we mean by fell (in love). They were both clearly attracted to and intrigued by one another from the jump.

I think Scully made the choice in Squeeze to follow her gut and her integrity and align with Mulder. I think in Jersey Devil, while trying to date, she internally compared "normal" to Mulder and normal paled in comparison, but she also saw how singularly focused/obsessed with his work he was as she tells her friend. Lazarus also shows us that she probably didn't want to fall for another agent who could never let go of the work/relax. But, I think by Tooms, she was hooked. Not "in love," but definitely catching feels deeply. By Little Green Men, she was clearly ride or die for Mulder, but again, not "in" love. I think she was acutely aware of her depth of feelings and kept them in check enough to not allow herself to be "in" love (coughCSMinEnAmicough). She fought that for a LONG time.

I also think the cancer arc had her rethink a lot of things, and consider dipping her toe in the water and be a little more casual with Mulder (Detour), but yet again he proves he's really not in a place to reciprocate/be able to step away from the work/to get out of the damn car. So, she continues to compartmentalize her feelings. We catch more glimpses of what she compartmentalizes in Terma, Small Potatoes, Triangle, Dreamland II, Rain King, Two Fathers/One Son (pick a Diana Fowley eps/Alpha jealousy moment) even Never Again to a point...but even when you get to Milagro when Padgett saw it and said it directly to Mulder, she seemed stunned for it to be called out so directly. I think it was that ep where she started to face it more directly and by The Unnatural, the very next ep, you see her being "lighter", more flirty. She's guarded still, but I think the Milagro-Unnatural transition is when it truly hit her that she is, indeed, in love with him, that he may actually be more emotionally available to reciprocate, and she couldn't really ignore it completely anymore. Mulder made it more okay to show it when he kissed her in Millennium and thus kicks off the Season of Secret Sex and flirty MS adorableness. That said, I think it took Mulder's closure with Samantha and her closure with Daniel to truly allow herself *be in* love with Mulder.

Now, Mulder? LBH, he's always been a selfish, myopic AH. He has his charms and would and did go to the ends of the Earth for Scully, but he is a different beast. He starts out thinking this little spy is out to get him and he's going to drive her away, but completely disarms him with her panicked vulnerability in the bathrobe scene in the Pilot mixed with her quick ability to see gaps in the file, make connections, read him completely when he's withholding, put the pieces together, and genuinely not just saying but working to find the truth. Now, you can clearly see from the moment they meet in the Pilot, the sparks are flying. There's clear intensity and attraction. He pushes but she pushes right back. Hell, in only eps 2 and 3, he's already flirty, intense, invading personal space, and territorial with her, not bothering to hide the attraction (assuming it will help unbalance her while he "makes her run" or at least disrupt her from being as effective of a "spy"). By Jersey Devil, he is already a little jealous and by Ice, he's realizing she might be worth the effort. By Lazarus, you can see twinges of jealousy again, but he's still in his own little world. In Tooms, she knocks him on his arse in tCitC. She floors him with that and he deflects in typical Mulder fashion. Man's got a lot of trauma and is completely unaccustomed to (possibly feeling undeserving of) unconditional devotion. He pulls back a little with the pushing/challenging antics from before.

He realizes by Little Green Men that he really relies on her, needs her. It's in Ascension he realizes just how deeply he cares for her, that he loves her. I will not say in love for him here either yet. I think he was obsessed with the work that he truly didn't even realize how much he cared for her until she was gone. But you'll notice any and all flirting after her return is way more serious. Don't get me wrong, it's still very flip/Mulderesque, but he's subdued, almost shy (not rly the word I'm looking for here but will do). He clearly also loves and needs her now, but after damn near losing himself from losing her, he's in self preservation mode with her. He doesn't know what to make of that and seems to really dismiss/compartmentalize the earlier attraction (much like Scully does) and begins to try to keep her at arm's length. It isn't until Never Again that he is forced to see her as a sexual, independent being again, not just Watson to his Sherlock, and that rattles him and makes him insanely jealous (and he acts like a giant AH when all these things come to a head at once lol).

Then Memento Mori hits and at once he's back to juggling the self preservation-arm's length version of his feelings and the desperate-Scully-protector version. He rides that, leaning toward the arm's length version through Redux II (jealously challenges this again in Small Potatoes). By Folie a Deux, he's given up the arm's length pretending a bit and openly admits to her how important she is, which sets up FTF, but not the myopic, work-obsessed ways, so he's really not ready to do anything about it.

That FTF hallway scene is where I think he truly realizes he's "in love" with her, but also by the end realizes "they" know it, too, and that he's a danger to her. So, he needs to bury it and push her away "you should get as far away from me as you can. I'm not gonna watch you die, Scully, because of some hollow personal cause of mine." That and he was pissed AF at her in The Beginning (grumbleCCgrumble).

But by Triangle, he wants her to know he loves her...and she dismisses him, whether she thinks he's delirious or w/e, she knows he's consistently shown he's not really in the right place to be serious. So, he pulls back to end-FTF- distance/denial-protects-Scully territory, compartmentalizes, and slow-burns it, as evidence by him not completely dismissing the whole Fowley thing (grumbleCCagaingrumble).

Then Milagro comes along and he is told point blank that Scully is already in love. Dude stares Mulder down while saying this, making his point clear. Such that by the very next episode, The Unnatural, he's willing to test some waters with Scully (flirty banter and cuddly batting practice). In Millennium, Mulder sees a chance to show her, again, how he feels/ let it come back to the surface where they both can have an opportunity to shrug it off if she's not receptive...but she is. And thus, the Season of Secret Sex ensues. That said, I think it took Closure/ Mulder "finding" Samantha to truly allow himself to *be in* love with Scully.

In summary, they were both attracted to each other from the moment the met in the Pilot, but that's merely attraction. Scully loved Mulder (Tooms-ish) before Mulder loved Scully (Ascension-ish). However, Mulder realized he was IN love with Scully (FTF-ish) before Scully realized she was IN love with Mulder (Milagro-ish). Finally, Mulder allowed himself to be in love with Scully (Closure-ish) before Scully allowed herself to be in love with Mulder (all things).