  This paper deals with a new analytic type of vector- and Clifford algebra
valued automorphic forms in one and two vector variables. For hypercomplex
generalizations of the classical modular group and their arithmetic congruence
subgroups Eisenstein- and Poincar\'e type series that are annihilated by Dirac
operators, and more generally, by iterated Dirac operators on the upper
half-space of $R^n$ are discussed. In particular we introduce (poly-)monogenic
modular forms on hypercomplex generalizations of the classical theta group.
