In this paper we study the behaviour of conjugacy functors in projective special linear groups PSL(2,p^f), p a prime, f a positive integer. Precisely, we find the primes q dividing the order of the group, whose relative conjugacy functors in PSL(2,p^f) control strong fusion, transfer, or weak closure of elements in the group. Such study is carried out first in the simple groups PSL(2,p^f), p ≠ 2, p^f > 3, and PSL(2,2^f), f > 1; finally we make a short remark on the solvable groups PSL(2,3) and PSL(2,2).