We consider a bound state problem for a family of supersymmetric gauge theo
ries with fundamental matter. These theories can be obtained by a dimension
al reduction of supersymmetric QCD from three dimensions to 1 + 1 and subse
quent truncation of some of the fields. We find that the models without adj
oint scalar converge to well-defined continuum limits and calculate the res
ulting spectra of these theories. We also find the critical value of coupli
ng at which an additional massless state is observed. By contrast, the mode
ls containing adjoint scalars seem to have a continuous mass spectrum in th
e limit of infinite volume.