It is demonstrated that the use of two coaxial solenoids instead of one in the magnetic field sensor cell allows one to divide the dynamic range of the magnetometer into a wide range of support magnetic field and a narrow range of bias field. This makes it possible to design, on the basis of a Hall sensor, a two-stage magnetometer with resolution of about 8·10 –11 Т. An increase in the speed of the magnetometer is achieved due to the use of a weak bias field, which represents a decaying oscillating local magnetic field (DOLMF). The leading edge of the DOLMF is used to search for a signal to be measured by a servo-system, while its decaying part after switching off the magnetic field step does not lead to magnetic relaxation in the sensitive element made of a superconducting YBa 2 Cu 3 O 7– x epitaxial film due to the fast process of vortex–antivortex annihilation. The design of the proposed magnetometer provides a high-speed measurement of not only constant but also alternating magnetic fields in the range from 10 –11 to 10 –7 Т at a frequency of up to ∼1 kHz, while preserving the high performance of the magnetometer. With the use of high-frequency magnetic field transducers, the magnetometer can operate in the frequency range of up to ∼100 kHz and measure both alternating and pulsed magnetic fields. • The use of two coaxial solenoids allows the design of a two-stage magnetometer with high resolution. • A superconducting epitaxial YBCO film is used as the sensitive element of the magnetometer. • The magnetometer provides a high-speed measurement of both constant and alternating magnetic fields.