IGLO calculations of the magnetic susceptibility tensors as well as of the C-13 and H-1 shielding tensors are performed and analyzed for benzene (1), the hypothetical cyclohexatriene (2) with alternating single and double bonds, some benzene isomers like fulvene (3), and other related molecules, including ethylene (8), the two 1,3-butadienes (9,10), and eight hexatrienes (11-18). The susceptibilities of the noncyclic polyenes as well as the benzene isomers 4 and 5 are rather well described by an increment system both for the in-plane and out-of-plane components, that of benzene only for the in-plane component, while for the out-of-plane component there is an additional shielding of 42 ppm cgs, which is reduced to 33 ppm cgs in cyclohexatriene. The other two molecules of this study with a somewhat enhanced out-of-plane susceptibility are fulvene (13 ppm cgs) and cyclopentadiene (17 ppm cgs). Evidence is accumulated that the increased susceptibility in benzene comes from the pi-electron system and is an indication of a nearly-free circular current in the pi-system of benzene. This becomes particularly manifest if one uses the center of the molecule as a gauge origin for the zz-component of the shielding due to the occupied pi-MOs. For this gauge the shielding is almost entirely diamagnetic, as required for a free current. In cyclohexatriene this current is somewhat attenuated, as seen from larger paramagnetic contributions. The increased susceptibilities in fulvene and cyclopentadiene are also due to the pi-system, though no genuine ring current effects can be detected. In the case of the H-1 shielding a different mechanism is responsible for the deshielding in ethylene (and polyenes) with respect to methane (or paraffins) and for the extra deshielding in benzene relative to ethylene. The latter is due to the occupied pi-MOs and related to the ring current. It is calculated to be similar to 5 ppm in the out-of-plane component, but it is reduced to less than 2 ppm in the isotropic shielding. Ring current effects are not detectable in any other molecules of this study, but in complementary investigations of other Huckel or anti-Huckel annulenes. The C-13 shift tensors show a very complicated pattern with large variations already between the isomeric hexatrienes, which are hard to interpret within an increment system. While the shift tensors in fulvene don’t differ too much from what one expects for carbon atoms in a similar bonding situation, bis-(methylene)cyclobutene and tris(methylene)cyclopropane are affected by strong ring strain effects. Benzene differs from polyenes mainly in a shielding of the out-of-plane component that is unusually strong for a CH carbon in an unsaturated system. Conclusions on a ring current effect would be premature.