  We start the study of the enumeration complexity of different satisfiability
problems in first-order team logics. Since many of our problems go beyond DelP,
we use a framework for hard enumeration analogous to the polynomial hierarchy,
which was recently introduced by Creignou et al. (Discret. Appl. Math. 2019).
We show that the problem to enumerate all satisfying teams of a fixed formula
in a given first-order structure is DelNP-complete for certain formulas of
dependence logic and independence logic. For inclusion logic formulas, this
problem is even in DelP. Furthermore, we study the variants of this problems
where only maximal, minimal, maximum and minimum solutions, respectively, are
considered. For the most part these share the same complexity as the original
problem. An exception is the minimum-variant for inclusion logic, which is
DelNP-complete.
