The present research investigated the importance of learning-related and interpersonal aspects of social competence as well as parent education in the first grade for school adjustment indicators These included self-reported involvement in bullying, teacher-reported student-teacher relationships, and academic achievement -- a year later. Social competence of children was assessed using the "Elementary School Social Competence Scale" (short version) completed by teachers. The sample consisted of 403 children attending 14 elementary schools in Lithuania. Results indicated that the learning-related aspect of social competence measured in the first grade was significantly related to all indicators measured in the second grade, while the interpersonal aspect of social competence was significantly related to student-teacher relationship quality. Taken together, both aspects of social competence assessed in the first grade explained some 34% of the variance in student-teacher conflict a year later. Interpersonal social competence explained 24% of the variance in student-teacher closeness. Furthermore, learning-related social competence and parent education significantly predicted academic achievement, accounting for 26% of the variance. Results of the present study highlight the lasting links of learning-related social competence and school adjustment indicators in elementary school.