Recently, Mao [9] initiated the study of exponential stability of neutral stochastic functional differential equations (NSFDEs) and [10] employed the Razumikhin techniques to investigated the stability problem of NSFDEs. However, the importance of general asymptotic stability has not been considered. This paper studies Razumikhin-type theorems on general pth moment asymptotic stability of NSFDEs. The theorems established in this paper work for some cases to which the existing results cannot be applied.