Contrary to previous replies - you do NOT need mode S for TCAS II to work, you will get RA's if both aircraft are fitted with mode C transponders only. What you get with Mode S is complementary RA's, ie, there is no possibility of both aircraft being given the same instruction.
Under Mode C only, it is possible for both aircraft to be given a climb or descent, but its rare and even then will resolve itself quickly as when the relative positions change one of the aircraft will then change its command.