This paper describes a scheme for automatically determining whether a problem can be solved more efficiently using a class of methods suited for nonstiff problems or a class of methods designed for stiff problems. The technique uses information that is available at the end of each step in the integration for making the decision between the two types of methods. If a problem changes character in the interval of integration, the solver automatically switches to the class of methods which is likely to be most efficient for that part of the problem. Test results, using a modified version of the LSODE package, indicate that many problems can be solved more efficiently using this scheme than with a single class of methods, and that the overhead of choosing the most efficient methods is relatively small.