Using the electron-spin-resonance technique we investigate the magnetic structure of CuCrO₂, a quasi-two-dimensional antiferromagnet with a weakly distorted triangular lattice. Resonance frequencies and the excitation conditions in CuCrO₂ at low temperatures are well described in the frame of cycloidal spin structure, which is defined by two susceptibilities parallel and perpendicular to the spin plane (χ_S and χ) and by a biaxial crystal-field anisotropy. In agreement with the calculations, the character of the eigenmodes changes drastically at the spin-flop transition. The splitting of the observed modes can be well attributed to the resonances from different domains. The domain structure in CuCrO₂ can be controlled by annealing of the sample in a magnetic field.