[en] In addition to the normally observed conduction-band--to--acceptor and ground-state-donor--to--acceptor transition peaks in the low-temperature photoluminescence spectrum of high-purity GaAs and InP, we report for the first time the observation of an additional peak in the spectrum, which we attribute to transitions from donors in their first excited state to neutral acceptors. This peak appears between the normally observed conduction-band--to--acceptor (e-A⁰) and ground-state-donor--to--acceptor (D/sub n/ = 1⁰-A⁰) peaks. The theory of Kamiya and Wagner is generalized to include this process and predicts line shapes in excellent agreement with experiment