We give a systematic treatment of the spin excitations of a family of disordered quasi-two-dimensional Heisenberg antiferromagnets, Rb2MnxNi1−xF4, for arbitrary values of x. The density of states, static response functions, and the dynamic susceptibility are calculated numerically. Results at several concentrations are presented graphically. We derive simple analytic theories which give an adequate description of the calculated quantities. The static response functions characterize excitations at low energy and long wave length, and enable us to predict the concentration dependence of the anisotropy gap frequency and the temperature dependence of the magnetization. The dynamic susceptibility is in good agreement with recent neutron-scattering experiments on Rb2Mn0.5Ni0.5F4. The spin-wave density of states for 0.1