The problem of poiesis of compact highly-sensitive magnetic-field sensors operating in a wide range of frequencies and amplitudes of the measured fields as well as having both a narrow radiation pattern and a low-temperature drift is actual and requires search for new magnetic materials and development of new principles of such sensors. The results on the development of compact highly-sensitive fluxgate sensors with magnetic core of amorphous foil of the MM-3Co and MM-5Co cobalt alloys and magnetoelectric sensors based on the martensitic single crystal NiMnGa are presented in this paper. The fluxgate sensors have high sensitivity, $k > 0.1$ V/Oe, with a low threshold of sensitivity, $\gamma < 10^{-9}$ nT/Hz, and can be used to measure both the direction and the magnitude of magnetic field in a wide range of the alternating magnetic-field spectrum from 0 to 106 Hz. The magnetoelectric sensors with sensitivity $k > 0.01$ V/Oe allow us to measure the magnetic field of medium and high values simultaneously on two coordinates in a quite wide range of frequencies.