Earlier measurements of the self-diffusion coefficients of 1-alkyl-3-methylimidazolium (or [RMIM], R = alkyl) tetrafluoroborates and hexafluorophosphates have been revised and extended to 90 degrees C. The main changes are to DS+ and DS- for [HMIM][PF6] ([C(6)C(1)Im][PF6]) and DS- for [OMIM][BF4] ([CsC(1)Im][BF4]). New atmospheric pressure self-diffusion, density, and conductivity data are provided for [HMIM] [BF4] ([C(6)C(1)Im] [BF4]). Velocity cross-correlation, distinct diffusion, and Laity resistance coefficients have been calculated. There is no evidence for ion association. A new relation between the Nernst-Einstein deviation parameter (Delta) and resistance coefficients (r(ij)) is derived; Delta tends toward 0.5 when the like-ion r(ii) are much smaller than the unlike-ion r(ij) i.e., when the counterion interactions dominate. [OMIM](+) ion salts approach this limit. Stokes-Einstein-Sutherland and Walden plots overlap almost quantitatively for [BF4](-), [PF6](-), and Cl- salts with a common [RMIM](+) cation. That is, in thermodynamic states that have the same viscosity, the salt molar conductivities and hence ionic electrical mobilities of, say, [BMIM][BF4] and [BMIM][PF6] are almost equal, as are the corresponding Brownian or diffusive mobilities, (D-S1/RT), for the cation, and also for these three small anions.