Simulation of QCD and other similar theories

In QCD one can change the representation of the gauge group for quarks and/or the gauge group itself. Examples of such generalizations are: (a) supersymmetric Yang-Mills theory with gauge group SU(2) or SU(3); (b) QCD with SU(2) colour and quarks in the adjoint representation; © QCD with three equal-mass quarks. Experience and perspectives in simulations of these theories by applying the two-step multi-bosonic algorithm is described. As an example of an interesting physical problem in these theories the expected spontaneous CP-violation in QCD with three equal-mass quarks is discussed.