We report experimental demonstration of graphene modelocked operation of Tm3+:YLiF4 (YLF) and Tm3+:KY3F10 (KYF) lasers near 2.3 mu m. To scale up the intracavity pulse energy, the cavity was extended, and double-end pumping was employed with a continuous-wave, tunable Ti3+:sapphire laser delivering up to 1 W near 780 nm. The extended Tm3+: KYF laser cavity was purged with dry nitrogen to eliminate pulsing instabilities due to atmospheric absorption lines, but this was not needed in the case of the Tm3+:YLF laser. Once initiated by graphene, stable uninterrupted mode-locked operation could be maintained with both lasers. With the extended cavity Tm3+:YLF laser, 921 fs pulses were generated at a repetition rate of 17.2 MHz at 2304 nm. 739 fs pulses were obtained at the repetition rate of 54 MHz from the Tm3+:KYF laser at 2340 nm. The corresponding pulse energy and peak power were 2.4 nJ and 2.6 kW for the Tm3+:YLF laser, and 1.2 nJ and 1.6 kW for the Tm3+:KYF laser. We foresee that it should be possible to generate shorter pulses at higher pump levels.