Confirmatory Factor Analysis was used to test first- and second-order factor models on cognitive abilities and their invariance across male and female samples. Subjects were a stratified random sample of 234 male and 225 female 15-year-old students in Singapore attending Secondary 3 (the equivalent of grade 9). Four first-order factors were found underlying the 23 subtest scores of 2 group intelligence tests, the AH(sub 4) Test of Intelligence and the Advanced Progressive Matrices, and 2 group Piagetian tests, Science Reasoning Tasks and the Arlin Test of Formal Reasoning. Slight differences found in the formal operations, spatial, numerical, and verbal factors of the male and female groups suggest some gender-related differences in these factors. There were two alternative second-order general factor models for the male group, one with three first-order factors and the other with four first-order factors. Only a general factor model with three first-order factors could fit the data of the female sample. This female group model contains some differences in the loading of the formal operations and spatial factors, when compared with that of the male group. Eight tables present study findings. (Author/SLD)