The article aims to study the verbal collaborative interaction in both symmetrical and asymmetrical dyads according to specific individual cognitive competence. The interaction was analyzed in terms of cognitive and non-cognitive aspects. 19 dyads (38 fifth and sixth graders) participated. First, they individually solved a set of logical problems to determine the initial level of competence. According to the outcomes, symmetric (both subjects of low level of competence) and asymmetric (one subject of low level of competence with one subject of high level of competence) dyads were made up. Second, they collaboratively resolved an equivalent set of problems. The collaborative interaction of the dyads was analyzed by a system of categories of three inclusive levels: (1) if messages were cognitive or non-cognitive; (2) it they were also affirmations, questions or answers; (3) if both cognitive affirmations and answers (both cognitive) were argumentative or non-argumentative. General outcomes showed that the asymmetry of epistemic competence was related to disequilibrium in the amount of messages and cognitive affirmations, especially argumentative, (but not in the rest of categories) in favor of the individual of higher level of competence. On other hand, symmetrical dyads showed equitable interactions related to all categories. A complementary analysis which consisted in an identification of more specific case differences related to modalities of interaction showed specific types of dyads within the general tendencies mentioned.