Hard real-time systems require both functionally correa executions and results that are produced on time. This means that the task scheduling algorithm is an important component of these systems. In this paper, efficient scheduling algorithms based on heuristic functions are developed to schedule a set of tasks on a multiprocessor system. The tasks are characterized by worst case computation times, deadlines, and resources requirements. Starting with an empty partial schedule, each step of the search extends the current partial schedule with one of the tasks yet to be scheduled. The heuristic functions used in the algorithm actively direct the search for a feasible schedule, i.e., they help choose the task that extends the current partial schedule. Two scheduling algorithms are evaluated via simulation. For extending the current partial schedule, one of the algorithms considers, at each step of the search,aZZ the tasks that are yet to be scheduled as candidates. The second focuses its attention on a small subset of tasks with the shortest deadlines. The second algorithm is shown to be very effective when the maximum allowable scheduling overhead is fixed. This algorithm is hence appropriate for dynamic scheduling in real-time systems.