Summary: Under a non-Lipschitz condition with the Lipschitz condition being considered as a special case and a weakened linear growth condition, the existence and uniqueness of mild solutions to stochastic neutral partial functional differential equations (SNPFDEs) is investigated. Some results of T. E. Govindan
[Stochastic Anal. Appl. 21, No. 5, 1059–1077 (2003; Zbl 1036.60052
); Stochastics 77, No. 2, 139–154 (2005; Zbl 1115.60064
)] are generalized to cover a class of more general SNPFDEs.