It is well known that the concept of left serial ring is a Morita invariant property and a theorem due to Nakayama and Skornyakov states that “a ring R is an Artinian serial ring if and only if all left R-modules are serial” and two theorems due to War?eld state that “a Noetherian ring R is serial if and only if every ?nitely generated left R-module is serial” and “a ring R is left serial if and only if every projective left R-module is serial”. We say that an R-module M is prime uniserial (?-uniserial, for short) if for every pair P, Q of prime submodules of M either P ? Q or Q ? P, and we say that M is prime serial (?-serial, for short) if it is a direct sum of ?-uniserial modules. Therefore, two interesting natural questions of this sort are: “Which rings have the property that every module is ?-serial?” and “Which rings have the property that every ?nitely generated module is ?-serial?”. It is shown that the ?-serial property is a Morita invariant property and also every projective left R-module is ?-serial if and only if R is a left ?-serial ring. In this thesis, we answer above questions in the case R is a Noetherian ring in which all idempotents are central or R is a left Artinian ring or R is a commutative ring. Another purpose of this thesis is to study what happens if, in the above Nakayama-Skornyakov Theorem, instead of considering rings for which all modules are serial, we consider rings for which every ?-serial (resp., ?-uniserial) module is serial (resp., uniserial). We answer these questions in the case R is a Morita equivalent to a Noetherian commutative ring or R is a Morita equivalent to a commutative ring.