The general problem addressed in this work is automatic identification of insects using only the acoustic modality. In particular, we discuss the characteristics of the acoustic profiles of two target groups of insects: crickets and cicadas. Subsequently, we employ advanced machine learning techniques to categorize them on the levels of specific insect, family, subfamily, genus, and species. To deal with the sparse spectral representation of some species, we adopt a score-level fusion of classifiers with non-parametric (probabilistic neural network) and parametric (Gaussian mixture models) estimation of the probability density function. We apply this approach to a large and well documented catalogue of cricket and cicada recordings, and we report identification accuracy that exceeds 99% on the levels of singing insect and family, and 90% on the level of a species out of 220 species.