The influence of strong pulsed magnetic fields on the martensitic transformation in steels and alloys, which are based on iron-nickel compositions with ‘invar anomalies’ of certain physical properties is analyzed. As shown, the anomalously large displacement of the martensitic point of some steels and alloys in strong pulsed magnetic fields at low temperatures is caused by magnetic first-order phase transition. This transition is caused by the rearrangement of the nonlinear magnetic structure of the $\gamma$-phase into a collinear one with a change in the coordination number when critical interatomic distance is reached as a result of the volume change that accompanies the paraprocess. Transformation of austenite to martensite by the type of magnetic first-order phase transition is also possible without a magnetic field if the critical interatomic distance is reached at the martensitic point due to spontaneous magnetostriction. This is possible when content of the main component—iron is high and the ratio of competing atoms of iron and nickel is optimal, as well as ‘catalyst’ (Cr, Mn) and elements that increase the interatomic distance (C, N) are present. It is assumed that the magnetic phase transition with a volume change occurs in the regions of magnetic-concentration inhomogeneities with a high content of iron atoms, which can be paramagnetic, antiferromagnetic or in the state of spin glass. The nucleation of martensite in case of the usual phase transition by athermic kinetics in steels and alloys of similar compositions, obviously, is based on the same inhomogeneities as in the magnetic first-order transition. Inhomogeneities that contain more Fe atoms than the average of the alloy, in themselves have a corresponding driving force, seeking to transit of f.c.c. in b.c.c. or b.c.t. structures.