K-homology is the dual theory to K-theory.The Baum-Douglas (BD) isomorphism of topological and analytic K-homology can be taken as providing a framework within which the Atiyah-Singer index theorem can be extended to certain non-elliptic operators.This talk considers a class of non-elliptic differential operators that arise on compact contact manifolds.These operators have been studied by a number of mathematicians.Working within the BD framework,the index problem will be solved for these operators.This is joint work with Erik van Erp.