The formation of kinetic, transient microstructures in structural phase transitions is analysed within the framework of time-dependent Landau-Ginzburg theories. The mesoscopic rate equation is delta phi / delta t= phi - phi 3+ delta 2 phi / delta x2- gamma delta ² phi / delta x⁴+ delta delta ⁶ phi / delta x⁶. A front of a stable state phi =1 can grow into an unstable region with phi =0 in an oscillatory manner. It will then leave behind a transient domain structure with quasi-periodic walls. Such domain structures occur for positive and negative values of gamma with sufficiently large values of mod gamma mod . The phase diagram in ( gamma , delta ) space is explored using computer simulation. The repetition length does not diverge at the bifurcation between an oscillatory and solitonic regime except at the point gamma =1/12. delta =0 studied previously. It is shown that recent computer simulation studies of "realistic" microstructures used implicit values of gamma and delta close to the bifurcation condition.