Four theoretical methods, using continuous transformation of the origin of the current density (CTOCD) to annihilate either the diamagnetic or the paramagnetic contribution, have been employed at the coupled Hartree-Fock level of accuracy to evaluate magnetic susceptibility and nuclear magnetic shielding of five planar molecules with the chemical formula C6H6. The results have been compared with corresponding estimates from basis sets of London orbitals, showing the near Hartree-Fock quality of calculated values and the practicality of CTOCD approaches. Maps of streamlines and intensity of the current density induced in the pi -electrons by a stationary magnetic-field perpendicular to the molecular plane are shown to interpret the different magnetic response properties of benzene isomers by means of the Ring-Current model. The plots show delocalized flow in benzene, determining its enhanced diamagnetism. Diamagnetic loops, localized in the region of carbon-carbon bonds, and a paramagnetic vortex in the vicinity of electronic centroid, are found in 3,4-dimethylenecyclobutene and trimethylenecyclopropane. This pattern is typical of conjugated nonaromatic molecules. Delocalized diamagnetic circulation observed in fulvene explains its exalted magnetic susceptibility.