Scientific and other grand challenge applications are a driving force for developing computing infrastructure of the future. Their constantly increasing computational power requirements often cannot be met by available systems [1]. Such a situation has led to the emergence of new platform called "Computational Grid" [2]. It seems very important to identify common and reusable components that are needed and can be used in a computational grid by different applications. Such components could be the Grid information services, security mechanisms, resource management, large data set management etc. This paper sketches the issues of one of the most important components of the grid - the resource management and scheduling component. We will present our work on multiobjective resource management system. The novelty of the approach lays in its multiobjective nature. We present the Multi-Criteria Resource Broker (MC-Broker), whose scheduling mechanisms are driven by the user preferences regarding various scheduling criteria, such as computation time and cost, communication time between distributed processes, level of load balancing and others.