The presented diagnostic study concerning intercultural competence was carried out in the pedagogical context of intercultural education. The research place was chosen purposively: it resulted from the intercultural character of Białystok. In the interwar period that the study refers to, the biggest national groups in the town were Poles and Jews. There were also Belarusians, Russians, Germans and Tatars. As part of the analysis of intercultural competence of students from Poland and Israel I focused on the respondents’ declarations concerning their knowledge of the social structure of pre-war Białystok. Then, I determined what motivates secondary school students to learn about the past. Developing the competence in the affective/motivational area is of key importance in intercultural communication. Identifying the reasons why secondary school students from Poland and Israel find it worth learning about the history of their ancestors is as important as knowledge of the history of our cultural group and other cultures. It was also important to determine the level of Polish youths’ readiness to communicate with students from Israel, and vice versa. Diagnosing the students’ competence allows educators to plan adequate educational activities aimed at broadening intercultural competence, to strengthen the existing resources, to improve the weak points, and fill in the gaps.