  We consider supermembranes ending on M5-branes, with the aim of deriving the
appropriate matrix theories describing different situations. Special attention
is given to the case of non-vanishing (selfdual) C-field. We identify the
relevant deformation of the six-dimensional super-Yang-Mills theory whose
dimensional reduction is the matrix theory for membranes in the presence of
M5-branes. Possible applications and limitations of the models are discussed.
