In this paper, we give an answer to the following question of I. Kaplansky[14] in the local case: For which duo rings R is it true that every nitely generated left R-module can be decomposed as a direct sum of cyclic modules? More precisely, we prove that for a local duo ring R, the following are equivalent:  (i) Every nitely generated left R-module is a direct sum of cyclic modules; (ii) Every 2-generated left R-module is a direct sum of cyclic modules;  (iii) Every factor module of RR  R is a direct sum of cyclic modules; (iv) Every factor module of RR  R is serial; (v) Every nitely generated left R-module is serial; (vi) R is uniserial and for every non-zero ideal I of R, R=I is a linearly compact left R-module; (vii) R is uniserial and every indecomposable injective left R-module is left uniserial; and, (viii) Every nitely generated right R-module is a direct sum of cyclic modules.