In this paper, we propose a multi-timescale replay (MTR) buffer for improving continual learning in RL agents faced with environments that are changing continuously over time at timescales that are unknown to the agent. The basic MTR buffer comprises a cascade of sub-buffers that accumulate experiences at different timescales, enabling the agent to improve the trade-off between adaptation to new data and retention of old knowledge. We also combine the MTR framework with invariant risk minimization, with the idea of encouraging the agent to learn a policy that is robust across the various environments it encounters over time. The MTR methods are evaluated in three different continual learning settings on two continuous control tasks and, in many cases, show improvement over the baselines.