Abstract: On a Kaehler manifold, the Hodge-Kaehler identities give a relationship between the commutator of the exterior derivative d and the Lefschetz operator L, and d^c, defined by conjugating d with the complex structure J. They are a fundamental tool to prove, for example, the equivalence of different Laplacians or the Lefschetz decomposition on Kaehler manifolds. There are generalizations of these identities for complex manifolds by Demailly, for almost Kaehler manifolds by De Bartolomeis and Tomassini, and for nearly Kaehler manifolds by Verbitsky. In this talk we will give a complete generalization, for almost complex manifolds, of the Hodge-Kaehler identities, and will find several other interesting commutator relations. The main technique is to prove a version of these identities in the Clifford bundle, using the Dirac operator instead of d, and then translate it to the exterior bundle. We expect that this technique can be used for other problems in complex and almost complex geometry. This is joint work with Samuel Hosmer.