A satisfactory theory of knowledge in which the shortcomings of a pure externalist account are avoided and in which the Gettier problem is solved should consist in a combination of externalist and internalist components. The internalist component should guarantee that the epistemic subject has cognitive access to the justifying grounds of her belief. And the externalist component should guarantee that the justification of her belief does not depend on any false statement. Keith Lehrer's coherence theory of knowledge as undefeated justification is an example of such an internalist-externalist analysis of knowledge. But nevertheless, Lehrer's account leads to unintended results. Therefore, it is argued that a satisfactory coherence theory of knowledge must also be based on a gradual notion of systematic coherence.