The present study aimed at investigating the acquisition process of number conservation by 2 training experiments. Ninety-eight 4-6 year-old children, who had been non-conservers at a Pre-test, served as Ss of Exp. I. Eighteen out of them could anticipate correctly changes of the number of a collection under transformations including addition and subtraction and spatial rearrangement of elements simultaneously. They were divided into a gr. and b gr.(Each had 9 Ss) The remaining 80 children could only anticipate numerical changes without spatial rearrangement. They were divided into a, b, c, d and e grs.(Each had 16 Ss) Each 2 children assigned to a and b gr. did not participate in the training session. Five different training procedures were adopted: Practice in conflict situations with external reinforcement (Ss of a and a grs. received this method of training), Practice in conflict situations without external reinforcement (b and b grs.), Practice in reinforced conservation situations (c gr.), Practice in mixed situations with reinforcement (d gr.), and Practice in conflict situations without reinforcement+ some auxiliary steps (e gr.). Each training procedure consisted of 2 sessions of 24 trials, and was given Ss on 2 consecutive days. Fourty-three Ss out of the 94 trained acquired conservation response, i. e., responded correctly to all of the conservation items (4 in number) at the Immediate Post-test. Thirty-nine of them retained conservation response at the Follow-up Test administered 50 days later. They were given a generalization test of conservation, including 3 types of conservation tasks i) extended in number of elements, ii) with the inequal standard collection and iii) without the standard collection, i. e., identityof a collection before and after rearrangement of elements. Twenty-six among them responded correctly to all of the items of the generalization test. Further, it was attempted to extinguish conservation response by false-reinforcement procedure similar to that of Smedslund. Twenty of them could not be deceived and retained conservation. c gr., a gr. and d gr. had more conservation respondents than the other 2 groups. d gr., a gr. and c gr. had more conservers who could apply the, conservation principle to the generalization test. a gr. and d gr. had slightly more Ss who showed resistance to extinction. These results suggest that conservation of number was diffcult to learn by Practice in conflict situations without external reinforcement. It is markedly different with previous studies by Smedslund and by us. At the same time, performance of children who had been superior at the Pretest(a & b), showed improvement of equal degree with and without reinforcement. External reinforcement had not a differentiating effect for them. It was assumed that, without external reinforcement, b & e grs. Ss continued to make perceptiondominated response to conflict situations because of insufficient coordination of inter-number relations. Therefore, Exp. II was undertaken, in which 2 training procedures were to be compared: Practice in conflict situations with and without external reinforcement, both having auxiliary steps for teaching inter-number relations with reinforcement. The result of Exp. II, however, showed ineffectiveness of Practice without reinforcement. Again, reinforced practice produced more conservers than the non-reinforced counterpart.