This paper is a contribution to the study of equality-free logic, that is, first-order logic without equality. We mainly devote ourselves to the study of algebraic characterizations of its relation of elementary equivalence by providing some Keisler-Shelahtype ultrapower theorems and an Ehrenfeucht-Fraïssé type theorem. We also give characterizations of elementary classes in equality- free logic. As a by-product we characterize thesentences that are logically equivalent to an equality-free one. © 1996 by the University of Notre Dame. All rights reserved.