The Hall effect in InMnAs layers with MnAs inclusions of 20-50 nm in size is studied both theoretically and experimentally. We find that the anomalous Hall effect can be explained by the Lorentz force caused by the magnetic field of ferromagnetic inclusions and by an inhomogeneous distribution of the current density in the layer. The hysteretic dependence of the average magnetization of ferromagnetic inclusions on an external magnetic field results in a hysteretic dependence of RH(Hext). Thus we show the possibility of a hysteretic RH(Hext) dependence (i.e. observation of the anomalous Hall effect) in thin conductive layers with ferromagnetic inclusions in the absence of carriers spin polarization.PACS numbers: 61.72.uj, 72.20.My, 75.50.Pp The investigation of the anomalous Hall effect (AHE) is a widely used experimental method for the diagnostics of the magnetic and transport properties of ferromagnetic layers, in particular, those of diluted magnetic semiconductors (DMS) [1]. In the conventional interpretation, the AHE is a consequence of an asymmetric scattering of spin-polarized charge carriers in ferromagnetic materials [2]. Thus the observation of the AHE is traditionally considered to be a proof of the presence of spin-polarized carriers. The spin polarization of carriers in DMS is usually attributed to a mechanism of indirect exchange interaction between transition metal ions via charge carriers [3,4]. In the high temperature region this mechanism should become slack [3,4]. However, the AHE was observed at room temperature or above in some Mn-doped semiconductors [5][6][7]. The AHE was also observed at about 300 K in Co-doped TiO 2 [8,9] and (La,Sr)TiO 3 [10] layers containing Co clusters. In Refs. [8-10] the appearance of AHE was related to spin polarization by extrinsic (induced by the clusters) spin orbit scattering. Earlier, it was also observed that in InMnAs layers obtained by laser deposition in gas atmosphere a clear hysteresis in the magnetic field dependencies of the Hall resistance manifests itself up to room temperature [11].In III-Mn-V layers the second-phase inclusions may appear during technology processes. In particular, nanosize ferromagnetic MnAs particles can be embedded in a semiconductor matrix [12,13] In this Letter, we present the results of theoretical and experimental investigations of the AHE in the InMnAs layers obtained by laser deposition. Nevertheless our results can be generalized to other conductive layers with ferromagnetic inclusions. Figure 1 shows the brightfield cross-sectional scanning transmission electron microscopy (STEM) image of the InMnAs/GaAs structure with Y Mn =0.2. The image reveals a phase inhomogeneity of the InMnAs layer. Figure 1 also shows the energydispersive X-ray spectroscopy (EDS) mapping of Mn, In and As in the structure. The bright areas in the Mn mapping image correspond to the regions of predominantly Mn atoms. At the same time these regions are free from In atoms. Taking into account the uniform distribution of As atoms it can be concluded ...