Current status of the research project APVV-0321-11 developing new types of semiconductor detectors of neutrons based on high quality 4H-SiC epitaxial layers will be presented. Recent studies show 4H-SiC as a suitable material for alpha, beta, X-ray, ion and neutron detection and spectrometry. Its high radiation and thermal hardness makes it one of the possible materials for fusion reactors. The main project objective is to measure the response to neutrons using prepared semiconductor detectors based on the 4H-SiC material with and without the conversion layer (HDPE and 6LiF) and compare the experimental results with simulations in the MCNPX code. In the project, we utilize our experience with bulk semi-insulating GaAs detectors of neutrons and compare both results obtained with SiC and GaAs detectors.