This paper introduces TestFul, a framework for testing stateful systems and focuses on object-oriented software. TestFul employs a hybrid multi-objective evolutionary algorithm, to explore the space of feasible tests efficiently, and novel quality metrics, based on both def-use pairs and behavioral coverage, to judge the quality of tests. We compare our framework against random testing by considering the level of coverage, the size of generated tests, and the time required to generate the tests. Our preliminary results show the validity of the approach: TestFul outperforms random testing in most of the cases. Categories and Subject Descriptors D.2.5 [Software Engineering]: Testing and Debugging Keywords Test Generation, Evolutionary Algorithms, Stateful Systems, Object-Oriented Paradigm, Multi-Objective Optimization General Terms Algorithms, Design, Experimentation