The report addresses the question of the structure of cognitive abilities, i.e., how many different abilities should be identified and the relations between abilities. Models suggested by Spearman, Thurstone, Guilford, Vernon, Cattell-Horn and others are reviewed. By combining features of the Vernon and Cattell-Horn models it is possible to construct a more general model, of which most other models are special cases. An empirical study is presented in which a test battery of 16 tests was administered to some 1200 pupils in the sixth grade. The test battery was designed to reflect the Cattell-Horn factors fluid intelligence (Gf), crystallized intelligence (Gc), and general visualization (Gv). A sequence of LISREL-models is presented in which the suggested model for the organization of abilities is tested. Good support is obtained for the model. In relation to interpretations of G (or Gf), it is proposed that this factor represents the ability to create and execute new assemblies of processes. Gc and Gv are interpreted to reflect the ability to process verbal and figural information, respectively, both as a function of the specific processing requirements posed by these types of information, and as a consequence of previously acquired knowledge. (Author/PN)