Two ionic liquids based upon N-alkyl-N-methylpyrrolidinium cations (PY(1R)(+)) (R=3 for propyl or 4 for butyl) and the bis(fluorosulfonyl)imide (FSI(-)), N(SO2F)2(-), anion have been extensively characterized. The ionic conductivity and viscosity of these materials are found to be among the highest and lowest, respectively, reported for aprotic ionic liquids. Both ionic liquids crystallize readily on cooling and undergo several solid-solid phase transitions on heating prior to melting. PY13FSI and PY14FSI are found to melt at -9 and -18 degrees C, respectively. The thermal stability of PY13FSI and PY14FSI is notably lower than for the analogous salts with the bis(trifluoromethanesulfonyl)imide (TFSI(-)), N(SO2CF3)2(-), anion. Both ionic liquids have a relatively wide electrochemical stability window of approximately 5 V.