The strategy of using generalized topologies and hereditary classes to extend classical topological concepts have been used by many mathematicians. In this work, we define and study the concepts of some generalizations of µ-lindelöf generalized topological spaces with respect to a hereditary class H, namely; nearly µ-lindelöf generalized topological spaces with respect to a hereditary class H. In addition, some basic properties of concepts are investigated, the relation among this work and some other generalizations of µ-lindelöf are shown