We propose a probabilistic framework to infer autosomal and sex-linked genes from RNA-seq data of a cross for any sex chromosome type (XY, ZW, UV). Sex chromosomes (especially the non-recombining and repeat-dense Y, W, U and V) are notoriously difficult to sequence. Strategies have been developed to obtain partially assembled sex chromosome sequences. Most of them remain difficult to apply to numerous non-model organisms, either because they require a reference genome, or because they are designed for evolutionarily old systems. Sequencing a cross (parents and progeny) by RNA-seq to study the segregation of alleles and infer sex-linked genes is a cost-efficient strategy, which also provides expression level estimates. However, the lack of a proper statistical framework has limited a broader application of this approach. Tests on empirical Silene data show that our method identifies 20 to 35% more sex-linked genes than existing pipelines, while making reliable inferences for downstream analyses. ~12 individuals are needed for optimal results based on simulations. For species with an unknown sex-determination system, the method can assess the presence and type (XY versus ZW) of sex chromosomes through a model comparison strategy. The method is particularly well optimised for sex chomosomes of young or intermediate age, which are expected in thousands of yet unstudied lineages. Any organisms, including non-model ones for which nothing is known a priori, that can be bred in the lab, are suitable for our method. SEX-DETector and its implementation in a Galaxy workflow are made freely available.