We report on our observations of the 79 and 119 mu m doublet transitions of OH for 24 local (z < 0.262) ULIRGs observed with Herschel-PACS as part of the Herschel ULIRG Survey (HERUS). Some OH 119 mu m profiles display a clear P-Cygni shape and therefore imply outflowing OH gas, while other profiles are predominantly in absorption or are completely in emission. We find that the relative strength of the OH emission component decreases as the silicate absorption increases. This result locates the OH outflows inside the obscured nuclei. The maximum outflow velocities for our sources range from less than 100 to similar to 2000 km s(-1), with 15/24 (10/24) sources showing OH absorption at velocities exceeding 700 km s(-1) (1000 km s(-1)). Three sources show maximum OH outflow velocities exceeding that of Mrk231. Since outflow velocities above 500-700 km s(-1) are thought to require an active galactic nucleus (AGN) to drive them, about two-thirds of our ULIRG sample may host AGN-driven molecular outflows. This finding is supported by the correlation we find between the maximum OH outflow velocity and the IR-derived bolometric AGN luminosity. No such correlation is found with the IR-derived star formation rate. The highest outflow velocities are found among sources that are still deeply embedded. We speculate that the molecular outflows in these sources may be in an early phase of disrupting the nuclear dust veil before these sources evolve into less-obscured AGNs. Four of our sources show high-velocity wings in their [C II] fine-structure line profiles, implying neutral gas outflow masses of at least (2-4.5) x 10(8) M-circle dot.