This work presents a new possibility of registration of ionizing radiation by the flowing gaseous radiochemical method (FGRM). The specified method uses the property of some solid crystalline lattice materials for a free emission of radioactive isotopes of inert gas atoms formed as a result of nuclear reactions. Generated in an ampoule of the detector, the radioactive inert gases are transported by a gas-carrier into the proportional gas counter of the flowing type, where the decay rate of the radioactive gas species is measured. This quantity is unequivocally related to the flux of particles (neutrons, protons, light and heavy ions) at the location of the ampoule. The method was used to monitor the neutron flux of the pulsed neutron target "RADEX" driven by the linear proton accelerator of INR RAS. Further progress of the FGRM may give rise to possible applications in nuclear physics, astrophysics and medicine, in the nondestructive control of fissionable materials, diagnostics of thermonuclear plasma, monitoring of fluxes and measurement of spectra of bombarding particles.