  A novel class of integrable surfaces is recorded. This class of O surfaces is
shown to include and generalize classical surfaces such as isothermic, constant
mean curvature, minimal, `linear' Weingarten, Guichard and Petot surfaces and
surfaces of constant Gaussian curvature. It is demonstrated that the
construction of a Backlund transformation for O surfaces leads in a natural
manner to an associated parameter-dependent linear representation. The
classical pseudosphere and breather pseudospherical surfaces are generated.
