The viscosity and density of melts of composition close to primary olivine tholeiite and alkali olivine basalt have been measured at pressures between 0.7 and 1.5 GPa and at temperatures between 1300¿ and 1475¿ using the falling/floating sphere method. The viscosity of the olivine tholeiite melts decreases only slightly from 1 atm to 1.0 GPa, whereas that of the alkali olivine basalt melts decreases by a factor of about 2 in the same pressure range, and they become very close to one another (about 2.0 Pas) at 1.0--1.25 GPa at 1400¿ C. The activation energy for viscous flow of the olivine tholeiite melt is about 250 ksJ/mol at 1.0 GPa. The viscosity of partial melts (melts formed by partial melting) in the upper mantle can be estimated based on the viscosities of the melts and the activation energy for viscous flow obtained by the present experiments. The viscosity of the partial melts along the anhydrous solidus of peridotite decreases from about 2.5 Pa s at 0.8 GPa (1220¿ C) to only about 0.2 Pa s at 3.5 is GPa (1580¿ C). Thus, the partial melts must be extremely fluid at depths greater than 100 km even under anhydrous conditions. Such partial melts might not ascend because of their high density and play an important role in the movement of the lithosphere. The viscosities of the partial melts in the upper mantle may decrease with increasing depth until completion of the transformation of Si to six-fold coordination. The viscosities of magmas and the diffusivity of oxygen in them have an inverse relation, which is approximated by the Eyring's equation. The diffusivity of oxygen in the partial melts, estimated from this relation and the viscosity, increases from 10-7 cm2/s at 0.8 GPa to 10-5 cm2/s at 3.5 GPa along the anhydrous solidus of peridotite. Homogenization of partial melts or magmas would be greatly enhanced with increasing depth down to the viscosity minimum.