Summary: As a continuation of our research for the Lorentz spaces defined by the Choquet integral, this paper is devoted to the study of the completeness and separability for the Lorentz spaces defined by the Sugeno and Shilkret integrals in the framework of nonadditive measure theory. It is also shown that the Lorentz spaces defined by the Sugeno integral coincide with the space of all Sugeno integrable functions and the Lorentz spaces defined by the Shilkret integral coincide with the Lorentz spaces of weak type.