•Two approaches are presented for the RUL prediction of products with two-phrase degradation.•The RUL under gamma process without degradation rate change is considerably underestimated.•The RUL prediction for a specific product can be obtained, although the rate change has not occurred.•The SEM yields relatively less bias and more reliable interval estimates.•The Bayesian approach requires less computational time. Remaining useful life prediction has been one of the important research topics in reliability engineering. For modern products, due to physical and chemical changes that take place with usage and with age, a significant degradation rate change usually exists. Degradation models that do not incorporate a change point may not accurately predict the remaining useful life of products with two-phase degradation. For this reason, we consider the degradation analysis for products with two-phase degradation under gamma processes. Incorporating a probability distribution of the time at which the degradation rate changes into the degradation model, the remaining useful life prediction for a single product can be obtained, even though the rate change has not occurred during the inspection. A Bayesian approach and a likelihood approach via stochastic expectation-maximization algorithm are proposed for the statistical inference of the remaining useful life. A simulation study is carried out to evaluate the performance of the developed methodologies to the remaining useful life prediction. Our results show that the likelihood approach yields relatively less bias and more reliable interval estimates, while the Bayesian approach requires less computational time. Finally, a real dataset on LEDs is presented to demonstrate an application of the proposed methodologies.