This paper defines and studies an approximation algorithm for scheduling tasks with small communication delays on m processors starting from a schedule σ∞ for the problem instance with an unlimited number of processors with relative performance bounded by α. This solution is used to solve the resource conflicts during the scheduling phase on m processors. A mechanism for UET–UCT tasks systems is first presented and analyzed. Then a rather unusual feature is introduced to handle SCT task systems: a processor may remain idle even if some tasks are feasible in order to wait for a more important task. The schedule generated by this algorithm is proved to have an overall worst-case performance $1+(1−1/m)\alpha$. If the best-known ratio $\alpha = \frac{4}{3}$ is used it induces a worst-case performance bounded by $\frac{7}{3} - 4 / m$ for our algorithm.