Fine magnetic-and microstructures in CoNiGa magnetic shape memory alloy single crystals were generated by applying pulsed magnetic fields of up to 0.7 T. The effects observed could be attributed to a change in the dynamics of the interaction process between the magnetic field and the microstructure of the offstoichiometric sample. This report addresses the impact of pulsed magnetic fields on the structure and phase composition in CoNiGa and multicomponent (CoNiCu)(AlGaIn) alloys. A pulsed magnetic field can result in different microstructural accommodation processes in stress-induced martensite, as compared to the application of mechanical stress or a permanent magnetic field. In a pulsed magnetic field the development of new nano-twin systems in the martensitic structure of the CoNiGa alloy and the formation of fine magnetic domains at the microscale, as well as the evolution of this process, in (CoNiCu)(AlGaIn), were observed. The ramifications of exploiting pulse magnetic fields for magnetic shape memory in these compounds will be discussed.