A bicomplex is a simple mathematical structure, in particular associated wi
th completely integrable models. The conditions defining a bicomplex are a
special form of a parameter-dependent zero-curvature condition. We generali
ze the concept of a Darboux matrix to bicomplexes and use it to derive Back
lund transformations for several models. The method also works for Moyal-de
formed equations with a corresponding deformed bicomplex.