Outstanding Li+ conductivity and diffusivity have been achieved in free-standing ion gel electrolytes synthesized by in-situ photopolymerization of 1-(2-methacryloyloxy)ethyl-3-butylimidazolium bis(trifluoromethane sulfonyl) imide (IMMA) and/or poly(ethylene glycol) methacrylate (EGMA), in the presence of the room temperature ionic liquids 1-ethyl-3-methylimidazolium bis(fluorosulfonyl)imide (EMIFSI), 1-butyl-1-methylpyrrolidinium bis(fluorosulfonyl)imide (BMPFSI) and bis(trifluoromethane)sulfonimide lithium salt (LiTFSI). The membranes are easy to handle and thermally stable up to 200 ºC. Those containing IMMA in the polymer chain present liquid-like ionic conductivities (up to 10 mS cm−1 at 25 ºC), and liquid-like Li+ diffusivities and conductivities (DLi≈4×10−11 m2 s−1, σLi≈1.4 mS cm−1 at 25 ºC) unreported so far in a solid electrolyte. DLi is not only very high but significantly higher than its counteranions’ diffusivity, DFSI or DTFSI, a very rare behavior in electrolytes where transport is, in principle, ruled by viscosity. It is proposed that in these polycationic electrolytes the motion of Li+ occurs via two different transport mechanisms, the well-known viscosity-governed transport and an additional anion-exchange mechanism that enables very fast Li+ diffusion. This combination has high practical relevance for Li+ batteries as it implies a high contribution of σLi to the overall electrolyte’s conductivity, and it constitutes a breakthrough in the design of polymer-based solid electrolytes for Li.