The response of a ferromagnetic system in which each electronic spin is coupled to a nuclear spin on the same site and to a microwave-frequency uniform magnetic field is studied. Using an effective-field approximation to decouple the equations of motion, we find an absorption when the rf field is parallel to the magnetization. In the case in which the finite-q magnon width is dominated by the exchange-induced four-magnon confluence process, this absorption peaks at the frequency ωu+AaSza. Here A is the hyperfine coupling constant, aSza is the magnetization in units of spin per site, and ωu is the frequency of the uniform spin-wave mode. We compare the results of the theory with the experiments of Jeffries and Ford on K2CuCl4•2H2O in which a line with many of the predicted features was observed. Theory and experiment agree on the following features: the dependence of the intensity on magnetic-field direction, the magnitude of the intensity and its dependence on temperature, and the high-temperature magnitude and temperature dependence of the width. The reported dependence of the experimental line intensity on the frequency of the rf field is not consistent with the present form of the theory. The relation of this kind of resonance to ordinary parallel pumping and another possible origin of the observed uniform-mode absorption are briefly discussed.