Equations are derived which describe the E.S.R. spectra of free radicals in solution when the spin exchange interactionJS1.S2provides the dominant relaxation mechanism. It is shown that modified Bloch equations provide an adequate description ifJis much greater than any frequency differences in the spectrum and the hyperfine interactions can be neglected during spin exchange collisions, but that in general the exchange rate depends on the frequency differences and spin de-phasing effects can occur even in the absence of spin exchange. Also, small shifts in resonance frequencies are shown to arise because of electron spin polarization in the applied field; but these are usually much smaller than the line widths.