We present the first examples of ab initio calculations of electron transition current density (TCD) maps in molecules. Expressions for TCD, derived previously, are implemented at the ab initio level for the pi-pi* transition in ethylene and the pi-pi* and n-pi* transitions in formaldehyde, with the CI-singles approximation for the excited states. The vector field calculations of the TCD were carried out utilizing an adaptation of Gaussian 92 and displayed with the AVS software program package. The TCDs can be viewed in various planes to achieve the perspective desired. In the case of the pi-pi* transitions, large vector-field components can be seen along the direction of the allowed electric dipole transition moment. Minor components perpendicular to the principal direction can also be seen, which integrate to zero over the volume of the molecule and do not contribute to the electric dipole transition moment. For formaldehyde, distinct contributions from pi-pi* and n(y) -3p(x) configurations are observed. For the n-pi* transition in formaldehyde, the magnetic dipole character of this transition is apparent from the circulation of TCD about the C=O bond axis at both the oxygen and the carbon centers. In addition, the electric quadrupole character of this transition is apparent in the xy-symmetric pattern of the TCD in a region midway along the C-O bond. We conclude that TCDs of electronic transitions provide new insight into the spatial character and composition of such transitions, which should prove useful in relating the results of quantum mechanical calculations to molecular electronic structure and dynamics.