We report unipolar resistive switching in ultrathin films of chemically produced graphene (reduced graphene oxide) and multiwalled carbon nanotubes. The two-terminal devices with yield >99% are made at room temperature by forming continuous films of graphene of thickness similar to 20 nm on indium tin oxide coated glass electrode, followed by metal (Au or Al) deposition on the film. These memory devices are nonvolatile, rewritable with ON/OFF ratios up to similar to 10(5) and switching times up to 10 mu s. The devices made of MWNT films are rewritable with ON/OFF ratios up to similar to 400. The resistive switching mechanism is proposed to be nanogap formation and filamentary conduction paths. (C) 2011 Elsevier Ltd. All rights reserved.