In this paper we address the effective use of the object-oriented programming approach for concurrent programming from a language design viewpoint. We present a set of requirements for the design of concurrent object-oriented languages. We then use a particular language, Hybrid, as a concrete example and examine to what extent its features meet these requirements. We identify the solutions offered by Hybrid and its shortcomings and we underline both the difficulties and promising directions for the design of concurrent object-oriented languages.