In this paper a rather general theory of oblique factor rotation is outlined. The main results are formulated as four theorems. Necessary and sufficient conditions are derived for two factor matrices to admit identical factor structures and/or factor patterns with factors having unit variances. These conditions are expressed in terms of eigenvectors and eigenvalues of certain matrices obtainable from the data. It is also shown that two matrices admitting identical factor structures will admit identical factor patterns and vice versa. After introducing the notion of a pair of transformations to identical structures and/or identical patterns, rules are given as to finding such pairs if they exist. Finally, some immediate consequences of the theorems are noted. They concern, for example, the suitable choice of a target structure and/or pattern and a hierarchical order of jointly necessary and sufficient conditions for fitting a specified target perfectly. (Author)