A presentation (X;R) of a group G is called diagrammatically aspherical (DA) if every identity sequence over it can be transformed to the empty sequence by the Peiffer operations of exchange and deletion alone, see \textit{I. M. Chiswell}, \textit{D. J. Collins} and \textit{J. Huebschmann} [Math. Z. 178, 1-36 (1981; Zbl 0443.20030)]. In the paper under review a certain class of presentations is considered where the generators are partitioned into disjoint subsets called types. If in addition each relator is cyclically reduced and involves exactly two types of generators, the presentation gives rise to a certain graph whose vertices are just the types, and each edge gives rise to what is called an edge presentation. The main theorem asserts that under suitable technical conditions the given presentation is DA if and only if so is each edge presentation. This result is then illustrated with a number of examples. \{Reviewer's remark: A complete argument that small cancellation presentations are DA was given in ref. [5] and not in ref. [4] as asserted in the paper.\}