Hydrogen pressure of 0.5-140 bar has been applied to synthesize hydrides of UCoGe. Besides an α hydride crystallizing in the structure type of the parent compound, which loses the weak ferromagnetism found in pure UCoGe, two distinctly different β hydrides were identified. The almost pure β hydride (UCoGeH(1.7)) is a ferromagnet below T(C) = 50 K. The highest H(2) pressures (> 130 bar) produce admixture of another hydride called β' hydride, with less H/f.u. and T(C) = 8 K, obtained presumably as a decay product of a full hydride UCoGeH(2.0) unstable at ambient conditions. The value of the Sommerfeld coefficient of electronic specific heat γ increases over 100 mJ mol(-1) K(-2) for the magnetic hydrides.