The microwave absorption spectrum of amorphous sputtered GdxAl1-x films at 9.13 GHz exhibits a single broad line which is studied as a function of temperature and composition x. In the paramagnetic regime, the g factor has a composition-independent positive shift of 0.006±0.004 above 1.992 of the free Gd3+ ion, in contrast to negative shifts previously reported for crystalline GdAl. The shift is interpreted as arising from an exchange interaction Jdf of the Gd f shell with electrons of d character. The g-shift contribution of the exchange interaction Jsf with s electrons is presumed to be hidden because of a "thermal bottleneck." This latter exchange interaction has a minimum value of 0.1 eV, as deduced from paramagnetic Curie temperatures. Using the observed temperature dependence of the resonance linewidth plus approximate band parameters from analogous dilute crystalline systems, the spin-lattice relaxation rate of amorphous GdxAl1-x is estimated to be 1013x Hz, in order-of-magnitude agreement with dilute crystalline systems. At lower temperature the field for resonance shifts down, strongly for x=0.37 but less strongly for higher Gd concentration. This shift is interpreted as an effective anisotropy field arising from local demagnetizing fields of an inhomogeneous (spin-glass) system. The composition dependence of the shift indicates that with increasing Gd concentration, the alloy becomes more magnetically homogeneous, gradually approaching simple ferromagnetism. © 1978 The American Physical Society.