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Viking Orbiter images of Phobos and Deimos have been measured to establish global control networks for 98 surface features of the former and 53 of the latter; photogrammetric triangulation has yielded body-fixed coordinates of these control-points, as well as mean triaxial radii of 13.3 x 11.1 x 9.3 km for Phobos and 7.5 x 6.2 x 5.4 for Deimos. Expressions are also obtained for the inertial orientations of these bodies' spin axes and prime meridians. While these expressions should be accurate to a few tenths of a deg for the 1971-1980 period, their accuracy will degrade with time as the orbit accuracy degrades.