Using conventional mental test theory, item parameters of an aptitude or achievement test vary with each group of examinees, and as such are somewhat limited in their use and interpretation. Within the last 25 years, measurement models have emerged in which item parameters are considered to be invariant. Generically referred to as latent trait mental measurement or item characteristic curve theory, these models have precipitated the development of sophisticated tailored testing techniques which capitalize on the item parameter invariance feature. This paper examines the invariance feature for the Birnbaum 2 and 3 parameter logistic models. The investigation is in two parts, the first theoretical, the second empirical. Even with somewhat inadequate data, the empirical investigation supported the theoretical considerations. (Author/RC)