Laser-ablated Zr and Hf atoms have been codeposited at 10-11 K with hydrogen (H-2, D-2, HD, H-2 + D-2) in excess argon. Infrared spectra revealed weak bands for the monohydrides, medium intensity bands for the dihydrides and trihydrides, and strong bands for the tetrahydrides. Identification of the latter is confirmed by observation of all four stretching modes of ZrH2D2 and HfH2D2 in the reactions with HD. Simple SCF calculations suggest that the ZrH2 + H-2 reaction is exothermic whereas the TiH2 + H-2 reaction is endothermic, which accounts for the domination of tetrahydrides in the Zr (and Hf) systems. The vibrational frequencies are higher for Hf hydrides (by 55-105 cm(-1)) than for Zr hydrides, owing to relativistic contraction, in agreement with calculations.