This paper deals with donor, acceptor-codoped (Ba0.4Sr0.6)TiO3 ceramics with distinct varistor characteristics at room temperature, which were prepared by single-step firing in air. The materials, with the Curie point at around -90 degrees C, exhibited a large PTCR (positive temperature coefficient of resistivity) effect of more than seven orders of magnitude in the temperature range -90 degrees C (the resistivity rho approximate to 10(3) Omega . cm) to room temperature (rho > 10(10) Omega . cm). An apparent dielectric constant of >20000 and tan delta < 0.05 (at 100 kHz) were observed for the present materials at room temperature, and moreover, the materials exhibited nonlinear current-voltage characteristics with the nonlinear coefficient, a, in the range 7-12 and the varistor field, E-v, in the range 0.3-1.0 kV/cm. The value of alpha in the present materials increased systematically with increasing rho in their PTCR temperature range. It has been found that there exists a close correlation between alpha and the grain-boundary potential barrier height, e phi, obtained from the rho-T characteristic of the materials. An almost linear relationship was also found to exist between alpha and log E-v for the present materials.