This paper is concerned with the debate in evolutionary epistemology about the nature of the evolutionary process at work in the development of science: whether it is Darwinian or Lamarckian. It is claimed that if we are to make progress through the many arguments that have grown up around this issue, we must return to an examination of the concepts of change and evolution, and examine the basic kinds of mechanism capable of bringing evolution about. This examination results in two (...) kinds of processes being identified, dubbed direct and indirect, and these are claimed to exhaust all possibilities. These ideas are then applied to a selection of the debates within evolutionary epistemology. It is shown that while arguments about the pattern and rate of evolutionary change are necessarily inconclusive, those concerning the origin of novel variations and the mode of inheritance can be resolved by means of the distinctions made here. It is claimed that the process of selection in the evolution of science can also be clarified. The conclusion is that the main process producing the evolution of science is a direct or Lamarckian one although, if realism is correct, an indirect or Darwinian process plays a vital role. (shrink)