J. L. Cabrerizo et al.  studied slant submanifolds of Sasakian and K- contact manifolds. Semi-slant submanifolds were introduced as a generalized version of CR-submanifold. Cabrerizo et al.  obtained interesting results for the semi-slant submanifold of Sasakian manifolds. The purpose of the present paper is to study slant and semi-slant submanifolds of a T-manifold.