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Heusler alloys have multifunctional properties that are important for a variety of practical applications. It determines the continuously growing interest in these systems. Ternary alloys of the Ni-Mn-X family, where X = Ga, In, Sb, and also quaternary alloys Ni-Mn-X-Z, of a certain concentration composition, experience a martensitic transition (MT) from a high-temperature cubic phase (austenite) into a low-temperature phase with tetragonal distortions (martensite). This transition can be magnetically induced, accompanied or not accompanied by a change in the magnetic order, and it is responsible for many properties, in particular, giant deformations, giant magnetocaloric effect, giant anomalous Hall effect (AHE), magnetic shape memory effect, etc. Recently, skyrmions and the corresponding topological Hall effect were found. in Ni-Mn-Ga and Ni-Mn-In alloys [1, 2]. The report analyzes experimental data on structural, magnetic and magnetotransport properties for several Heusler magnetic shape memory alloys with focus on behavior of NHE and AHE in a wide temperature range including MT. We studied Ni48Co2Mn35In15, Ni50Mn34.8In15.2, Ni50Mn35In15–xSix (x = 1.0, 3.0, 4.0), Ni50Mn35In15−xBx (x = 0, 0.5, 0.75), Ni45Cr5Mn37In13, Ni49BiMn35In15 bulk samples, fabricated by arc-melting, Ni47.3Mn0.6Ga22.1 and Ni49.7Fe17.4Co4.2Ga28.7 thin films, obtained by magnetron scattering. Normal and anomalous Hall effect coefficients were determined by fitting the field dependencies of the Hall resistivity using magnetization data. Our experimental data can be considered as an evidence of electronic structure transformation during MT with redistribution between spin-up and spin-down d-states and insignificant change of total density of states at the Fermi level.