The tidal evolution of planets orbiting brown dwarfs (BDs) presents an interesting case study because BDs' terrestrial planet forming region is located extremely close-in. In fact, the habitable zones of BDs range from roughly 0.001 to 0.03 AU and for the lowest-mass BDs are located interior to the Roche limit. In contrast with stars, BDs spin up as they age. Thus, the corotation distance moves inward. We study the tidal evolution of planets around BDs using a standard tidal model and test the effect of numerous parameters such as the initial semi-major axis and eccentricity, the rotation period of the BD, the masses of both star and planet, and their tidal dissipation factor. We find that the most important parameter is the initial orbital distance with respect to the corotation distance. We find that all planets that form at or beyond the corotation distance and with initial eccentricities smaller than about 0.1 and are repelled from the star. Some planets initially interior to corotation can survive if their inward tidal evolution is slower than the BD's spin evolution, although most initially close-in planets fall onto the BD. Next we studied multiple planet systems with a N-body code altered to include tidal forces. We present a few interesting case studies for systems of planets orbiting BDs. In one example, a close-in planet pushes a more distant planet outward while locked in resonance. In another example, rapid outward tidal migration destabilizes a system of three planets. In another case, the combination of eccentricity forcing from an outer planet and dissipation within the inner planet drives the inner planet into the BD despite being exterior to the corotation radius. We thank the CNRS's PNP program for funding.< Réduire