Sex chromosomes and sex determining genes can evolve fast, with the sex-linked chromosomes often differing between closely related species. Population genetics theory has been developed and tested to explain the rapid evolution of sex chromosomes and sex determination. However, we do not know why the sex chromosomes are divergent in some taxa and conserved in others. Addressing this question requires comparing closely related taxa with conserved and divergent sex chromosomes to identify biological features that could explain these differences. Cytological karyotypes suggest that muscid flies (e.g., house fly) and blow flies are such a taxonomic pair. The sex chromosomes appear to differ across muscid species, whereas they are conserved across blow flies. Despite the cytological evidence, we do not know the extent to which muscid sex chromosomes are independently derived along different evolutionary lineages. To address that question, we used genomic and transcriptomic sequence data to identify young sex chromosomes in two closely related muscid species, horn fly (Haematobia irritans) and stable fly (Stomoxys calcitrans). We provide evidence that the nascent sex chromosomes of horn fly and stable fly were derived independently from each other and from the young sex chromosomes of the closely related house fly (Musca domestica). We present three different scenarios that could have given rise to the sex chromosomes of horn fly and stable fly, and we describe how the scenarios could be distinguished. Distinguishing between these scenarios in future work could identify features of muscid genomes that promote sex chromosome divergence.