TWO DIFFERENT TYPES OF FACTOR MODELS ARE CONSTRUCTED FOR EXPLAINING A CORRELATION BETWEEN TWO VARIABLES. IN THE FIRST MODEL, IT IS SPECIFIED THAT THE CORRELATION BETWEEN OBSERVABLES IS DUE TO A SYNCHRONOUS COMMON FACTOR ONE THAT CONTEMPORANEOUSLY AFFECTS BOTH OBSERVABLES. IN THE SECOND MODEL, IT IS STATED THAT THE CORRELATION BETWEEN OBSERVABLES IS DUE NOT ONLY TO A SYNCHRONOUS COMMON FACTOR BUT ALSO TO A COMMON FACTOR THAT AFFECTS THE FIRST VARIABLE CONTEMPORANEOUSLY AND AFFECTS THE SECOND VARIABLE AFTER SOME DELAY. THIS SECOND VARIABLE IS A CROSS-LAGGED COMMON VARIABLE. THE OBJECTIVE IS TO FIND RESTRICTIONS ON OBSERVABLE CORRELATIONS THAT SERVE TO DISCRIMINATE BETWEEN THE TWO MODELS. TWO-WAVE TWO-VARIABLE MODELS, THREE-WAVE TWO-VARIABLE MODELS, AND TWO-WAVE MULTIVARIATE MODELS ARE EMPLOYED TO TEST FOR A SYNCHRONOUS COMMON FACTOR IN PANEL DATA. SUPPORTING EQUATIONS ARE INCLUDED IN THE TEXT OF THE ARTICLE AND IN AN APPENDIX. (DEP)