The conductivity of a concentrated cylindrical dispersion is evaluated theoretically. We show that the scaled conductivity (K*/K-infinity) approaches a constant value as kappa alpha --> 0, which depends on the scaled surface potential phi (r), where K*, K-infinity, kappa, and alpha are the apparent conductivity, the conductivity of an infinitely dilute dispersion; the reciprocal Debye length, and the radius of a cylinder. If kappa alpha --> infinity, K*/K-infinity also approaches a constant, but it is independent of phi (r). The effect of alpha (-valence of counterions/valence of co-ions) on K*/K-infinity is found to be significant if K alpha is small and becomes negligible as K alpha --> infinity. Also, if alpha > 1, K*/K-infinity decreases monotonically with the increase in K alpha, and the reverse is true if alpha < 1. If > 1, K*/K-infinity increases monotonically with phi (r), and the larger the alpha the faster the rate of increase. Also, if alpha < 1, K*/K- has a local minimum as phi (r) varies.