The previously developed two center shell model for symmetric fission has been extended to break-ups into unequal fragments. The potentials of the separate fragments have equal depth. The rounded barrier between them can have varying height. The two fragments can also have different deformations. Generalized l · s- and l 2-terms are included. This allows for the description of a great variety of nuclear shapes. The mathematical details are presented together with the analytically solvable matrix elements. For a few asymmetric fission processes the level spectra have been calculated.