  We introduce $(k,l)$-regular maps, which generalize two previously studied
classes of maps: affinely $k$-regular maps and totally skew embeddings. We
exhibit some explicit examples and obtain bounds on the least dimension of a
Euclidean space into which a manifold can be embedded by a $(k,l)$-regular map.
The problem can be regarded as an extension of embedding theory to embeddings
with certain non-degeneracy conditions imposed, and is related to approximation
theory.
