  We address the problem of defining graph transformations by the simultaneous
application of direct transformations even when these cannot be applied
independently of each other. An algebraic approach is adopted, with production
rules of the form $L\xleftarrow{l}K \xleftarrow{i} I \xrightarrow{r} R$, called
weak spans. A parallel coherent transformation is introduced and shown to be a
conservative extension of the interleaving semantics of parallel independent
direct transformations. A categorical construction of finitely attributed
structures is proposed, in which parallel coherent transformations can be built
in a natural way. These notions are introduced and illustrated on detailed
examples.
