A time-of-flight spectrometer of neutrons in the energy range (0.05 -2.5) µeV is described. This spectrometer has been tested my measuring the total and differential neutron cross sections for a number of materials: Al, Cu, 6 LiF, Si, Zr, teflon, polyethylene and liquid fluoropolymers, that are essential for experiments in the physics of ultracold neutrons.