One of the explanations which Streeter used to account for the minor agreements was an appeal to an overlap of sources: both Mark and Q might contain a particular section, and hence Matthew's agreements with Luke could stem from a Q source underlying them both. Many have felt that this theory constitutes a weakness for the 2DH, and others have claimed that the passages in question can be explained more easily by other hypotheses. Thus Devisch says:

The question to be discussed here is whether in fact these passages can be explained any more easily by other hypotheses, and in particular by the GH.

For the 2DH, the theory of overlapping sources gives rise immediately to interesting problems about the relationship between Mark and Q. If these two sources give two accounts of the same pericope, the question arises as to whether there is any relationship of literary dependence between them. Dependence of Q on Mark has rarely been advocated and is usually rejected. However, dependence of Mark on Q has often been advocated, either as dependence on a recension of Q slightly different from that known to Matthew and Luke, or on Q simpliciter.