The viscosity and relaxation time of polyelectrolyte solutions in high dielectric constant solvents are reported. The effects of polyelectrolyte concentration, polyelectrolyte charge density, solvent dielectric constant, solvent quality and salt concentration are well described by scaling theory. New data are presented for partially quaternized poly(2-vinylpyridine) in ethylene glycol (EG) and N-methyl formamide (NMF). EG and NMF are good solvents for the neutral polymer before quaternization, enabling the effects of polyelectrolyte charge density to be studied over an unusually wide range. EG also can be purified to have an unusually low concentration of salt ion contaminants, allowing dilute solutions of high molecular weight polyelectrolytes to be studied in the low salt limit (whereas this is impossible for all aqueous solutions and solutions in NMF). Hence, the scaling model can be fully tested in EG solutions. After multiple distillations, NMF has even larger quantities of residual salt than distilled water. However, just like aqueous solutions, the rheology of polyelectrolyte solutions in NMF can be understood by identifying the concentration at which the number density of free counterions equals the number density of salt ions. At higher concentrations, the NMF solution viscosity obeys the low-salt scaling predictions and at lower concentrations the viscosity obeys the high-salt predictions.