After consideration of the drawbacks of such psychometrically derived theories of cognitive abilities as those of Guttman, Cattell, and Guilford, appeal is made to E. B. Hunt's "distributive memory" model and A. Newell's concept of the "production system" as possible bases for developing an alternative theory. Such a theory of cognitive abilities nests upon the individual differences displayed in the parameters of the tasks found in typical tests of intelligence. It is hypothesized that factor-analytic common factors arise when two or more tasks share features in which there are individual differences with respect to (1) the types and contents of memory stores involved; (2) the types and sequences of cognitive operations required and cognitive strategies employed by individual subjects; and (3) the type of responses elicted. It is claimed that from this point of view cognitive tasks are complex and cognitive factors resist classification by any rigid taxonomy such as Guilford's Structure of Intellect model: there are probably no such things as truly "pure" factors. (Author/RC) (66pp.)