Mass movements of cytoplasm, known as cytoplasmic streaming, occur in some large eukaryotic cells. In Drosophila oocytes there are two forms of microtubule-based streaming. Slow, poorly ordered streaming occurs during stages 8-10A, while pattern formation determinants such as oskar mRNA are being localized and anchored at specific sites on the cortex. Then fast well-ordered streaming begins during stage 10B, just before nurse cell cytoplasm is dumped into the oocyte. We report that the plus-end-directed microtubule motor kinesin-1 is required for all streaming and is constitutively capable of driving fast streaming. Khc mutations that reduce the velocity of kinesin-1 transport in vitro blocked streaming yet still supported posterior localization of oskar mRNA, suggesting that streaming is not essential for the oskar localization mechanism. Inhibitory antibodies indicated that the minus-end-directed motor dynein is required to prevent premature fast streaming, suggesting that slow streaming is the product of a novel dynein-kinesin competition. As F-actin and some associated proteins are also required to prevent premature fast streaming, our observations support a model in which the actin cytoskeleton triggers the shift from slow to fast streaming by inhibiting dynein. This allows a cooperative self-amplifying loop of plus-end-directed organelle motion and parallel microtubule orientation that drives vigorous streaming currents and thorough mixing of oocyte and nurse-cell cytoplasm.