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The object of this work is to prove the following result: "Two oriented manifolds are cobordant if and only if all their Pontrjagin and Stiefel-Whitney numbers agree". This was conjectured by R. Thom and proved by C.T.C. Wall. Some consequences of this result are proved too. The following theoren of J. Milnor is showed: "Suppose that M is a n-dimensional oriented manifold. If M can be imbedded in euclidean space so as to have trivial normal bundle or if H_* (M:Z₂) is isomorphic to H_*(Sⁿ:Z₂) then M is a boundary.