We propose a method to investigate measurement invariance in the multigroup exploratory factor model, subject to target rotation. We consider both oblique and orthogonal target rotation. This method has clear advantages over other approaches, such as the use of congruence measures. We demonstrate that the model can be implemented readily in the freely available Mx program. We present the results of 2 illustrative analyses, one based on artificial data, and the other on real data relating to personality in male and female psychology students. (Contains 4 tables, 1 figure and 7 footnotes.)