  We investigate complement-finite submonoids of the monoid of nonnegative
integer points of a unipotent linear algebraic group $G$. These monoids are in
general noncommutative but they specialize to the generalized numerical monoids
of Cistco et al. We show that every unipotent numerical monoid has a unique
finite minimal generating set. We propose a generalization of the Wilf
conjecture in our setting. We contrast our Wilf conjecture against the
Generalized Wilf Conjecture. Then we isolate two new families of unipotent
numerical monoids called the {\em thick} and the {\em thin} unipotent numerical
monoids. We prove that our Wilf conjecture holds for every thick (commutative)
unipotent numerical monoid. Under additional assumptions on the conductors, we
prove that our Wilf conjecture holds for every thin (commutative) unipotent
numerical monoid.
