This paper studies the disjointness, the inclusion, and the regularity problem for nonterminating behaviors of concurrent systems modelled using Mazurkiewicz traces. The main finding is a trichotomy that, for every independence alphabet, determines the complexity of the problems (almost) completely. Noteworthy, for all the problems, the classes are the same. While these classes already appeared in the study of terminating behaviors, the trichotomy obtained here is more pronounced as the complexities vary from decidable via low levels of the arithmetical hierarchy to low levels of the analytical hierarchy (that do not feature in the result for terminating behaviors).