Some noncyclic small molecules, electrically neutral or charged, sustain interatomic electronic currents in the presence of a stationary, spatially uniform magnetic field. The existence of fairly large delocalized electron flow is demonstrated in H2O, BH3, NH3, CH4, CH3-CH3, H3O+, CH3+, and NH4+, by plots of quantum mechanical current density. Convincing quantitative evidence is arrived at by current strengths, defined via a flux integral of the ab initio current density. Application of a simple ring current model shows that the delocalized current strengths account for the out-of-plane component of the magnetic shielding tensor along the symmetry axis. A definition of delocalized electron current as a current flowing along a closed loop containing three or more atoms is discussed.