Their relationship?!? This time, no doubt, they are siblings!! Brother and sister! Monica is only one year younger than Ross!!!!

Season 1

Monica: Excuse me, where are you going?
Ross: Uh... to the bathroom.
Monica: Do you want to go to the bathroom, or do you wanna play poker?
Ross: I want to go to the bathroom. [exits]
Ep. 9 ~TOW All The Poker~

Season 2

ROSS: Tho?
(Monica shakes her head.)
ROSS: Ohhh.
MONICA: That's good, have a seat. Um, the doctor says it's gotta be a needle. You're just gonna have to be brave, ok? Can you do that for me?
ROSS: Ok.
MONICA: Ok. Oh boy. You are doin' so good. You wanna squeeze my hand? All right, Ross, don't squeeze it so hard. Honey, really, don't squeeze it so hard! Oh, Ross! Let go of my hand!
Ep. 6 ~The One With the Baby on the Bus~

ROSS: I just wanna thank you for being there for me today. And I'm sorry I,I almost broke your hand.
MONICA: That's ok. I'm sorry I poisoned you.
ROSS: Yeah. Hey, remember the time I jammed that pencil into your hand?
MONICA: Remember it? What do you think this is, a freckle?
ROSS: Oh.
MONICA: Wait, what about the time I hit you in the face with the Silvian's pumpkin?
ROSS: Oh, man. Oh, remember when I stuck that broom in your bike spokes, and you flipped over and hit your head on the curb?
MONICA: No. But I remember people telling me about it.
ROSS: I hope Ben has a little sister.
MONICA: Yeah. I hope she can kick his ass.
ROSS: I'm gonna get a new band-aid. Hey, how 'bout the time I cut the legs off your Malibu Ken?
MONICA: That was you?
ROSS: They, uh, were infected. He wouldn't have made it.
Ep. 6 ~The One With the Baby on the Bus~