Na+ and sugar permeabilities of egg lecithin bilayers were measured using curved bilayers and planar bilayers as represented by single-bilayer vesicles and black lipid films, respectively. The Na+ permeability coefficient measured with single-bilayer vesicles at 25 degrees C is (2.1 +/- 0.6) x 10(-13) cm sec-1. Because of technical difficulties it has been impossible to measure ionic permeabilities of values lower than about 10(-10) cm sec-1 in planar (black) lipid bilayers using tracer methods. The D-glucose and D-fructose permeabilities were measured with both curved and planar bilayers. The permeability coefficients measured with vesicles at 25 degrees C are (0.3 +/- 0.2) x 10(-10) cm sec-1 for glucose and (4 +/- 1) x 10(-10) cm sec-1 for D-fructose; these are in reasonable agreement with the corresponding values obtained for planar (black) lipid bilayers which are (1.1 +/- 0.3) x 10(-10) cm sec-1 for D-fructose, respectively.