  Generalized Lambda-semiflows are an abstraction of semiflows with
non-periodic solutions, for which there may be more than one solution
corresponding to given initial data. A select class of solutions to generalized
Lambda-semiflows is introduced. It is proved that such minimal solutions are
unique corresponding to given ranges and generate all other solutions by time
reparametrization. Special qualities of minimal solutions are shown. The
concept of minimal solutions is applied to gradient flows in metric spaces and
generalized semiflows. Generalized semiflows have been introduced by Ball.
