The purpose of this paper is to deepen the study of the Prufer ⋆–mul-tiplication domains, where ⋆ is a semistar operation. For this reason, we introduce the ⋆–domains, as a natural extension of the v-domains. We investigate their close relation with the Prufer ⋆-multiplication domains. In particular, we obtain a characterization of Prufer ⋆-multiplication domains in terms of ⋆–domains satisfying a variety of coherent-like conditions. We extend to the semistar setting the notion of $\texttt{H}$ -domain introduced by Glaz and Vasconcelos and we show, among the other results that, in the class of the $\texttt{H}(\star)$ –domains, the Prufer ⋆-multiplication domains coincide with the ⋆-domains. Keywords: Star and semistar operation, Prufer (⋆-multiplication) domain, $\texttt{H}$ -domain, Localizing system, Coherent domain, Divisorial and invertible ideal Mathematics Subject Classification (2000): 13F05, 13G05, 13E99