Pluto's surface is covered in numerous CH 4 ice deposits, that vary in texture and brightness, as revealed by the New Horizons spacecraft as it flew by Pluto in July 2015. These observations suggest that CH 4 on Pluto has a complex history, involving reservoirs of different composition, thickness and stability controlled by volatile processes occurring on different timescales. In order to interpret these observations, we use a Pluto volatile transport model able to simulate the cycles of N 2 and CH 4 ices over millions of years. By assuming fixed solid mixing ratios, we explore how changes in surface albedos, emissivities and thermal inertias impact volatile transport. This work is therefore a direct and natural continuation of the work by , which only explored the N 2 cycles. Results show that bright CH 4 deposits can create cold traps for N 2 ice outside Sputnik Planitia, leading to a strong coupling between the N 2 and CH 4 cycles. Depending on the assumed albedo for CH 4 ice, the model predicts CH 4 ice accumulation (1) at the same equatorial latitudes where the Bladed Terrain Deposits are observed, supporting the idea that these CH 4 -rich deposits are massive and perennial, or (2) at mid-latitudes (25 • -70 • ), forming a thick mantle which is consistent with New Horizons observations. In our simulations, both CH 4 ice reservoirs are not in an equilibrium state and either one can dominate the other over long timescales, depending on the assumptions made for the CH 4 albedo. This suggests that long-term volatile transport exists between the observed reservoirs. The model also reproduces the formation of N 2 deposits at mid-latitudes and in the equatorial depressions surrounding the Bladed Terrain Deposits, as observed by New Horizons. At the poles, only seasonal CH 4 and N 2 deposits are obtained in Pluto's current orbital configuration. Finally, we show that Pluto's atmosphere always contained, over the last astronomical cycles, enough gaseous CH 4 to absorb most of the incoming Lyman-α flux.