Background: The number of sequenced eukaryotic genomes is rapidly increasing. This means that over time it will be hard to keep supplying customised gene finders for each genome. This calls for procedures to automatically generate species-specific gene finders and to re-train them as the quantity and quality of reliable gene annotation grows. Results: We present a procedure, Agene, that automatically generates a species-specific gene predictor from a set of reliable mRNA sequences and a genome. We apply a Hidden Markov model (HMM) that implements explicit length distribution modelling for all gene structure blocks using acyclic discrete phase type distributions. The state structure of the each HMM is generated dynamically from an array of sub-models to include only gene features represented in the training set. Conclusion: Acyclic discrete phase type distributions are well suited to model sequence length distributions. The performance of each individual gene predictor on each individual genome is comparable to the best of the manually optimised species-specific gene finders. It is shown that species-specific gene finders are superior to gene finders trained on other species.