Peer mediation with young children is a relatively novel approach aimed at teaching young children how to mediate to their peers. The main benefits of peer mediation are in developing children's mediation teaching style and cognitive modifiability. The peer mediation developed recently is based on Vygotsky's sociocultural and Feuerstein's "mediated learning experience" theories. The main objectives of the study were to investigate the effects of the Peer Mediation with Young Children (PMYC) programme on children's cognitive modifiability of mediators and learners and to study the effects of cognitive level of the learner and mediator on their cognitive modifiability following the programme. A sample of 178 pupils (89 mediators in Grade 3 and 89 learners in Grade 1) was randomly assigned to experimental (N=43 dyads) and control (N=46 dyads) groups. The mediators in the experimental group participated in the PMYC programme, whereas the mediators in the control group received a substitute intervention aimed at emphasizing general conditions of peer interaction. Following the intervention, mediators of both groups received a demonstration of a multimedia programme as a preparation for the peer mediation interaction and later taught it to their young counterparts. Following the teaching session (e.g. teaching of seriation problems), mediators in both groups were given a dynamic assessment measure of analogies. The learners however were given a test of seriation before and after the intervention. The findings showed that following the intervention the experimental mediators showed higher level of analogies scores, as well as higher improvement on the dynamic analogies measure as compared with control mediators. The experimental learners showed higher pre- to post-intervention achievements on the seriation problems as compared with control learners. The findings showed also that when there was a match between the mediator and learner's cognitive level (i.e. low-low or high-high) the differences between the experimental and control groups were minor and negligible. However, when the mediator-learner cognitive levels did not match, the experimental learners received higher scores than the control learners. Mediators in the experimental group had to cope with the incongruent cognitive level by facilitating their mediational approach and consequently enhancing the learner's performance. The findings are discussed in regard to Piaget, Vygotsky and Feuerstein's theories and recent research on peer assisted learning.