We have measured the electron paramagnetic resonance (EPR) of Gd3+ in single crystals of La2-xSrxCuO4+δ, as a function of temperature T, magnetic-field angle, oxygen content, microwave frequency, and Sr concentration (0≤x≤0.024). For temperatures larger than the antiferromagnetic ordering temperature of the Cu lattice, TN, we have identified four different sites of Gd3+ as expected for twinned crystals and we are able to fit the data for all directions of the magnetic field. Samples annealed under vacuum or oxygen show only small changes on their crystal-field parameters and g values. For temperatures smaller than TN, the EPR lines are further split due to the internal magnetic field acting at the Gd site associated with the antiferromagnetic ordering of the Cu lattice. The temperature dependence of the splitting of the resonance lines allow us to calculate the moment per Cu ion. A value of ∼0.6μB per Cu ion at T=0 K is inferred, with the Cu moments lying in the bc plane about 5°from the c axis. The data only can be fit for all the directions of the applied magnetic field if other mechanisms such as a Heisenberg type of exchange between the Cu and Gd moments or a distortion of the lattice below TN are included. © 1993 The American Physical Society.