The flow of quasi-direct currents (QDCs) in AC electrical networks, is a disturbing factor that mainly prevails upon mutual impacts between different system components or due to geophysical phenomena. These QDCs can alter the normal behavior of the system components, e.g., power transformer inrush currents. In this paper, an analysis of the inrush current phenomenon in power transformers under the influence of QDCs has been performed. The effect of QDCs on power transformer inrush currents is first mathematically analyzed, and then investigated by computer simulations in EMTP-RV software. Results show that power transformer inrush currents can severely increase in the presence of QDCs.