---

There is a family of generalized Farlie-Gumbel-Morgenstern copulas, known as the semiparametric family, which is generated by a function called distribution-based generator. These generators have been studied typically for symmetric distributions in the literature. In this article, is proposed a method for asymmetric case which increases the flexibility of distribution-based generators and, thus, the model. In addition, a method for generalizing general generators is provided which can also be used to obtain more flexible distribution-based generators. Clearly, with more flexible generators more desirable models can be found to fit real data.