We study prime event structures as models for nondeterministic processes and some of their properties known as discreteness, density and crossing. These properties allow inconsistency to be avoided between syntactic and semantic representations of processes. A number close relationships between different density and crossing concepts is established. It has turned out that in an M-dense event structure all of the executions are completely "successful" (i.e. at least one successor (if it exists) for any event occurring in the execution must also occur).