In this paper, a system for overlapping acoustic event detection is proposed, which models the temporal evolution of sound events. The system is based on probabilistic latent component analysis, supporting the use of a sound event dictionary where each exemplar consists of a succession of spectral templates. The temporal succession of the templates is controlled through event class-wise Hidden Markov Models (HMMs). As input time/frequency representation, the Equivalent Rectangular Bandwidth (ERB) spectrogram is used. Experiments are carried out on polyphonic datasets of office sounds generated using an acoustic scene synthesizer-simulator, as well as real and synthesized monophonic datasets for comparative purposes. Results show that the proposed system outperforms several state-of-the-art methods for overlapping acoustic event detection on the same task, using both frame-based and event-based metrics, and is robust to varying event density and noise levels.