In this paper, we consider combining experimental and observational **data** for long-term causal inference. We are particularly interested in the challenge of potentially persistent confounding, i.e., unmeasured confounders that can affect both the short-term and the long-term outcomes. To overcome this challenge, we leverage the sequential structure of multiple short-term outcomes and use part of them as proxy variables for the unmeasured confounders. We propose three novel identification strategies for the average long-term treatment effect. Based on each of them, we design flexible treatment effect estimators and provide asymptotic guarantees. Our results show that the long-term treatment effect can be identified and estimated under much more general conditions than before.