Matrix strings in pp-wave backgrounds from deformed superYang-Mills theory

We formulate matrix models for strings in ten dimensional pp-wave backgrounds and for particles in eleven dimensional ones. This is done by first characterizing the deformations of ten dimensional Script N = 1 SYM which are induced by a constant bispinorial coupling ∫bar-ΨHΨ plus a minimal purely bosonic completition and then by the appropriate dimensional reduction. We find a whole class of new models for the matrix strings and a generalization of the supernumerary supersymmetric models as far as the matrix theory for particles is concerned. A companion deformation of the IKKT matrix model is also discussed.