Stress granules (SGs) and P-bodies (PBs) are related cytoplasmic structures harboring silenced mRNAs. SGs assemble transiently upon cellular stress, whereas PBs are constitutive and are further induced by stress. Both foci are highly dynamic, with messenger ribonucleoproteins (mRNPs) and proteins rapidly shuttling in and out. Here, we show that impairment of retrograde transport by knockdown of mammalian dynein heavy chain 1 (DHC1) or bicaudal D1 (BicD1) inhibits SG formation and PB growth upon stress, without affecting protein-synthesis blockage. Conversely, impairment of anterograde transport by knockdown of kinesin-1 heavy chain (KIF5B) or kinesin light chain 1 (KLC1) delayed SG dissolution. Strikingly, SG dissolution is not required to restore translation. Simultaneous knockdown of dynein and kinesin reverted the effect of single knockdowns on both SGs and PBs, suggesting that a balance between opposing movements driven by these molecular motors governs foci formation and dissolution. Finally, we found that regulation of SG dynamics by dynein and kinesin is conserved in Drosophila.