Different methods for indirectly establishing factor invariance across two situations both involving different individuals and different situations are out- lined. The procedures involve a planned data gathering strategy consisting of a t least two different groups, each receiving two different test batteries. The recommended strategy involves a combination of Tucker's interbattery technique and congruence measures. Some of the limitations of the concept of factor invariance are briefly discussed. It is concluded that statistical measures of factor invariance are a necessary but not a sufficient condition for the psycho- logical invariance of constructs accounting for individual differences.