This paper describes an Adaptive Implicit Method (AIM) for reservoir simulation. The method is based on an extension of the generalized compositional solution procedure. In addition to the creation of a robust method, we have tried to minimize the overhead associated with the method, so that our implementation is almost as fast as an IMPES (implicit-pressure-explicit-saturation) method when few implicit blocks are needed. Several test problems demonstrate important aspects of the switching logic and the tradeoffs between large highly implicit time steps and smaller time steps with less implicitness. We find that in most cases the greatest efficiency occurs when only a small number of blocks (less than 5 percent) are treated implicitly. In many cases the most efficient method is IMPES with time steps selected using the numerical stability calculations of AIM, Smaller time steps lead not only to higher efficiency, but also to solutions with less numerical dispersion. In general. AIM appears to benefit compositional problems more frequently than black oil problems.