In this paper, an approach to formally specify a conceptual model of a system and its environment to be developed in a behavior-oriented way is presented. We identify those concepts of object-oriented approaches that have to be formalized. We then propose characteristics of behavior-oriented mathematical models representing a system as a collection of interacting objects. To specify such models, we present the language \tt Oblog which is a formal object-oriented language for conceptual modeling. \tt Oblog avoids separate description of static and dynamic aspects of the system to be developed. Features of the language are explained using an example of a library information system.