The study of CR -submanifolds of a Kähler manifold was initiated by Bejancu [1]. Since then many papers have appeared on CR -submanifolds of a Kähler manifold. Also, it has been studied that generic submanifolds of Kähler manifolds [2] are generalisations of holomorphic submanifolds, totally real submanifolds and CR -submanifolds of Kähler manifolds. On the other hand, many examples C 2 of generic surfaces in which are not CR -submanifolds have been given by Chen [3] and this leads to the present paper where we obtain some necessary conditions for a generic submanifolds in a locally conformal Kähler manifold with four canonical strucrures, denoted by P , F , t and f , to have parallel P , F and t . We also prove that for a generic submanifold of a locally conformal Kähler manifold, F is parallel iff t is parallel.