The numerical solution of partial differential equations (PDEs) is the most computeintensive part of most scientific computer simulations, with applications in all fields of science and engineering. Consequently, improving the methods for solving PDEs has been the focus of much research in numerical methods for several decades. In the last two decades it has been shown that the combination of adaptive grid refinement and multigrid solution, known as adaptive multilevel methods, provide effective methods on sequential computers. Adaptive grid refinement reduces the problem size by focusing the effort to the regions where higher resolution is needed. In the last decade, research has been performed on parallelizing these procedures. Effective parallelization is difficult because of the irregular nature of adaptively refined grids. In this talk we present the coarse-grain algorithm for adaptive refinement used in the parallel adaptive multilevel program PHAML. The algorithm uses only two communication steps during an adaptive refinement phase. Adaptive refinement can be performed by each processor in parallel without communication until the very end. The algorithm is identical to the sequential algorithm except that only the elements in the partition owned by the processor, and those needed for compatibility of the grid, are candidates for refinement. This can be achieved by setting the refinement error indicator to zero outside the partition. A communication step at the end informs other processors of any elements that were refined outside the partition to insure that the owner of that element also refines it. A second communication step enforces an overlap requirement needed for fast convergence of the parallel multigrid algorithm. Results of numerical experiments on a cluster of eight PCs will be presented. These results demonstrate 60–90% parallel efficiency.