  The notion of a pseudocycle is introduced by McDuff and Salamon
(J-holomorphic curves and quantum cohomology, University Lecture Series, Vol.
6, AMS (1994)) to provide a framework for defining Gromov-Witten invariants and
quantum cohomology. This paper studies the bordism groups of pseudocycles,
called pseudohomology groups. These are shown to satisfy the Eilenberg-Steenrod
axioms. For smooth compact manifold pairs, it is proved that pseudohomology is
naturally equivalent to homology. Easy examples show that this equivalence does
not extend to the case of non-compact manifolds.
