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Powerful extragalactic water masers appear to be closely associated with active galactic nuclei: each of the 13 sources with apparent luminosity $L > 35\lsol$ presently known is a galaxy showing evidence for nuclear activity (Braatz \etal 1994, \apj in press). VLBI observations of 3 H$_2$O megamasers indicate that the masing regions lie $\sim 0.1$ pc from the nuclei. These water megamasers are plausibly produced via heating of dense circumnuclear gas by X-rays from an active nucleus (Neufeld, Maloney, \& Conger 1994, \apj in press). The number of OH megamasers is considerably larger ($\sim 50$) but the physical situation is less clear. All of the powerful OH masers lie in infrared-luminous galaxies, and it has been suggested that the OH megamasers arise by low-gain amplification of the central radio continuum source by gas distributed within a few hundred parsecs of the infrared source; the inversion of the OH levels is produced by the dust infrared continuum. However, VLBI observations of the prototype OH megamaser, Arp 220, show that most of the emission arises within 10 pc of the double nuclei, whereas only $\sim 1\%$ of the radio continuum comes from this region (Lonsdale \etal 1994, {\it Nature} 370 , 117). Furthermore, there is a marked anticoincidence: there are no OH megamasers which are also H$_2$O megamaser sources. H$_2$O megamasers generally show large OH absorption columns.
We show that these observational results can be understood if the OH megamasers also arise in near-nuclear dense gas irradiated by an active nucleus. The controlling parameter in determing whether an OH or H$_2$O megamaser will be produced is the gas pressure. At relatively low pressures ($P/k\lta 10^9\;{\rm cm^{-3} \ K}$) OH will be much more abundant than H$_2$O and an OH maser can be produced through pumping by the dust infrared continuum. At higher pressures, the water abundance becomes large enough that luminous H$_2$O maser emission can be generated; although the OH abundance is still substantial, the OH rotational levels are thermalized by collisions and OH masers cannot occur.
