A general description of the electrolytic conductivity behavior of highly charged strong polyelectrolytes in dilute and semidilute aqueous solutions is presented. For the first time this model considers the influences of the molar mass, charge density (for charge distances less than the Bjerrum length), polyelectrolyte concentration, and the ionic strength adjusted by both the polyelectrolyte concentration (c(p) in monomol L-1) and added simple salt concentration (c(s) in mol L-1). Above the overlap concentration (c*) the molar mass influence is weak. Below this overlap concentration the equivalent conductivity (Lambda) increases strongly with decreasing c(p), as long as c(p) > c(s). Correlations could be established for the maximum of Lambda, Lambda(max) similar to c(s)(-1/5) and Lambda(max) similar to M-2/5. The conductivity behavior can be qualitatively explained in terms of Manning＇s theory with an additional change of the interaction parameter f(c). On the basis of this fact an empirical dependence of f(c) on the ratio of the Debye length to the contour length (l(D)/L) has been found. Three concentration regimes differing in the polyion-counterion interaction could be identified. These are characterized by l(D)/L located below (4 pi)(-1/2), between (4 pi)(-1/2) and unity, and above unity, respectively. The model description includes polyelectrolyte solutions without added salt as well as solutions with any ratio of polyelectrolyte to salt concentration. This is the first model which is based on sufficient experimental data in the highly diluted concentration regime. Therefore, it should stimulate further theoretical studies.