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An $𝒮$-closed submodule of a module $M$ is a submodule $N$ for which $M/N$ is nonsingular. A module $M$ is called a generalized CS-module (or briefly, GCS-module) if any $𝒮$-closed submodule $N$ of $M$ is a direct summand of $M$. Any homomorphic image of a GCS-module is also a GCS-module. Any direct sum of a singular (uniform) module and a semi-simple module is a GCS-module. All nonsingular right $R$-modules are projective if and only if all right $R$-modules are GCS-modules.