The present article tests a proposed model of linear syllogistic reasoning on both determinate and indeterminate linear syllogisms. The proposed model, which includes processes acting upon both linguistic and spatial representations for information, is shown to be able to account for solution latencies from both kinds of linear-syllogism problems. These demonstrations of the internal validity of the model are accompanied by a demonstration of its external validity whereby composite and component scores for individual subjects are correlated with scores from verbal, spatial and abstract reasoning tests. A number of significant and substantial correlations confirm the relationships of components of the proposed mixture model to performance on tasks quite different in surface structure from the linear syllogisms. It is concluded that although the proposed model is not the true one (in that it does not account for all of the reliable variance in the latency data), it provides a good approximation to the strategy many subjects use in the solution of linear-syllogism problems.