This paper focuses on the invasion by Turbinaria ornata (a brown algae) in the Tuamotu archipelago, French Polynesia [(5–35°S)/(200–230°E)]. Prior to 1980, this alga existed only in the Society and Austral archipelagoes. Between 1985 and 1990, it began to appear in the southern and northern parts of the Tuamotu archipelago. Genetic analyses have been shown not to be appropriate in determining the origin of this algae population. This study investigated the possible ocean drift of floating aggregates of algae. Ocean currents were calculated from satellite data from 1993 to 2001. Their spatial variations as well as their seasonal and interannual variations are described along with calculated drift trajectories. While it was found that mean currents cannot directly transport algae from the Society and Austral archipelagoes to the Tuamotu, the large interannual changes during the El Niño-Southern Oscillation phenomenon produce current reversals that are strong enough to create a transport pathway in a short enough time to allow their survival.