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Almost analytic vectors and almost analytic tensors were studied by M. Ako, S. Koto, I. Sato, S. Sawaki, S. Tachibana, K. Yano and others. In the present paper we define contravariant almost analytic vector fields in the strict sense. A contravariant vector field u is almost analytic in the strict sense when u is almost analytic in the ordinary sense and, moreover, u satisfies Nj% u = Q where Nji is the Nijenhuis tensor of the almost complex structure. An almost analytic tensor field in the strict sense is similarly defined. As a consequence of such definition we can treat these vector fields and tensor fields in a unified form. We also find that almost analytic tensors always appear in couples. In the last section some local property of an integral manifold of a distribution associated with contravariant almost analytic vector fields is studied. Let M be a C°° manifold of dimension 2n admitting an almost complex structure /. The components of / are denoted by Fj when we use natural frames associated with local coordinates ξ, where indices such as h, i, j, k run over the range 1, ~ ,2n. Let Nμ be the Nijenhuis tensor of P\, hence

On some almost analytic tensor fields in almost complex manifolds