The free solution electrophoretic mobilities of poly(styrenesulfonate), ss-DNA, and duplex DNA are measured by capillary electrophoresis across a range of ionic strengths and, for poly(styrenesulfonate) and ss-DNA, across a range of chain lengths. The data are then compared with mobilities reported in the literature and predicted by theory. For ionic strengths below 0.1 M, the capillary method is more accurate and rapid than previous techniques; it also provides a distribution of mobility values for polyelectrolyte mixtures. A maximum of the free solution mobility with respect to chain length is discovered in the oligomer range for both poly(styrenesulfonate) and ss-DNA; lowering ionic strength accentuates this unexplained phenomenon. In the large chain limit, where the mobility is independent of chain length, the ionic strength dependences of mobility for all three polymers are remarkably similar. These dependences can only be explained by models that incorporate nonlinear electrostatic effects into the description of the counterion cloud. The Manning model (with relaxation correction) best approximates the dependence of mobility on ionic strength.