The Swedish school system has had a long tradition of equality and later on, equivalence, where the municipalities have a large responsibility as well as freedom in ensuring that children receive an equivalent education. During some time however, results have shown an increased importance of aspects such as family background and residential segregation for the children’s performances and hence a failing equivalence. The research question for this paper is: How do municipalities interpret their national obligation of ensuring equivalence in school? By preforming case studies in three municipalities with three different organizations, written sources and interviews allow for an in-depth analysis of the organizations in relation to equivalence. Looking at the challenges for an equivalent school today in combination with theories about equality in opportunity and equality in outcome, an analytical tool is created which is used to analyze the municipalities in a comparable way. This paper shows how the interpretations of the national obligation of ensuring equivalence in the three municipalities can be understood in regards to two dimensions – to what extent a municipality is compensating for the children’s family background in their organization and if the municipality prioritize an individual or a collective understanding of equivalence in their organization. The paper illustrates how a to vague legislation about equivalence may lead to very different organizations that in turn may threaten the national goal of equivalence.