A theory of weakly nonlienar low-temperture relaxational absorption f acosutic and electromagnetic wdaves in dielectric and metallic glasses isdevleoped. Basedupon te mdoel fo two-level tuneling systems we sdhwo that the nonienar contriubtion to the adbsorption k can be anomalously large. Tis is the case at wo enough frequencies, ωτ//0(T)<<1, where τ//0(T) is the miniml relaxation tiemf fortwo-level systems with te itnelrevel splitting ～k//BT. in dielectric glasses, the lwoest-roder noninear contribution is proportional to the wave's intenstiy. It i negativ eand exhbitis anomalous frequency and tmeruatre dependenes, ΔΓ/Γ//0∝[ωτ//0(T)]^-1/2 T^-2. in metallic glasses, the nonienar contribution is also negative, and it i proportional to the square root of the wav'es intensity and independent of the frequency. Nuemrical estiamtes shwo that the rpedicted nonlienar conribution can be measured experiemtnally. Kirkengen, M. Galperin, Yu. M.