The paramagnetic resonance spectrum of copper acetate is anomalous in that it resembles that of an ion of spin 1, and its intensity decreases as the temperature is lowered. The latter is correlated with the decreasing susceptibility found by Guha (1951). The following hypotheses are suggested: (1) the crystalline field acting on each copper ion is similar to that in other salts such as the Tutton salts; (2) isolated pairs of copper ions interact strongly through exchange forces, each pair forming a lower singlet state and an upper triplet state, the latter only being paramagnetic. On this basis both the fine structure and the hyperfine structure of the spectrum have a simple explanation, and the theory also predicts a small initial splitting of the triplet state of the same order as that found experimentally. The unit cell of the crystal contains two differently oriented pairs of ions, and, using an empirical value for the exchange parameter, fair agreement with the susceptibility measurements of Guha is obtained.