  We investigate continuity properties of operators obtained as values of the
Weyl correspondence constructed by N.V. Pedersen (Invent. Math. 118 (1994),
1--36) for arbitrary irreducible representations of nilpotent Lie groups. To
this end we introduce modulation spaces for such representations and establish
some of their basic properties. The situation of square integrable
representations is particularly important and in the special case of the
Schr\"odinger representation of the Heisenberg group we recover the classical
modulation spaces used in the time-frequency analysis.
