High-resolution spectra are obtained for the free A and B excitons in CdS by two-photon absorption photoconductivity techniques at 1.8 K. At zero applied magnetic field, spectra are shown which indicate for the first time the presence of anisotropy splitting of the B(2P) exciton states. The first observation of the B(3P) exciton state at B=0 T then allows the conclusion that both the effective Rydberg and the anisotropy parameter of the A and B excitons are the same. This further indicates that the A and B valence-band masses are equal. These conclusions are confirmed by the first observation of the Zeeman splitting of the B(2P±1) and B(3P±1) exciton states at fields up to 10 T. Fine-structure splitting of the B(2P+1) and B(2P-1) states results from an effective g factor for the B valence band of ghB=0.7±0.3. © 1983 The American Physical Society.