In this article, facing the gaps that the traditional long short-term memory (LSTM) and convolution neural network (CNN) cannot differentially deal with the input data based on the corresponding trend and stage information in remaining useful life (RUL) prediction, a more accurate and robust RUL prediction model is constructed. First, a temporally multidifferential LSTM (TMLSTM) with the multitrend division unit and multicellular unit is proposed, and a spatially multidifferential CNN (SMCNN) with the multistage division unit and differentiated convolutions is designed. Then, by combining TMLSTM and SMCNN, a spatiotemporally multidifferential deep neural network is developed for predicting the equipment RUL, which enhances the ability of feature extraction from the spatiotemporal perspective by using the multitrend and multistage information. Via several evaluation indexes, the commercial modular aero propulsion system simulation dataset and the wind turbine gearbox bearing dataset are used to validate the superiority of the proposed method over several existing prediction methods.