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This paper uses the Postnikov decomposition of a nonsimple fibration to describe the obstructions to a tangent 2-field on an even-dimensional nonorientable manifold. Our purpose in this article is to prove the following theorem. Main Theorem. Let M be a closed, nonorientable manifold of dimension m, where m is even and m > 2. Let %(M) in Hm(M; ZW¡<M)) and sl£m_x(M) indoi:10.1090/s0002-9947-1982-0648087-9 fatcat:cv2bjpyev5h5dmbmlug4kwwwpi