The current strategies for testing object-oriented software all lack the formal basis which is necessary to perform this task efficiently. We propose the adaptation to object-oriented software of an existing theory of testing for stateless ADTs, to find errors in a class by checking that its implementation meets its specification. We present shortly in an informal way an object-oriented language, CO-OPN/2, in which language we will write the specification. We introduce a notion of test that takes into account the possible and impossible sequences of call of class methods. We examine the black-box test procedure, and give techniques to select a finite and pertinent test set from an exhaustive test set, including all the possible behaviors of the class under test, by applying test reduction hypothesis. We also study the construction of an oracle, the procedure that analyses the results of the tests, adapted to object-oriented software.