We have developed approximate P-wave reflection moveout formulas for a homogeneous layer of orthorhombic symmetry overlying a horizontal or dipping reflector. The symmetry planes of an orthorhombic medium in the layer can be arbitrarily oriented. The formulas are based on the weak-anisotropy approximation. Thus, their accuracy depends not only on the strength of anisotropy, but also on the deviations of the phase and ray velocities. Nevertheless, the performed tests indicate that for P-wave anisotropy of approximately 25%, the maximum relative traveltime errors of the formulas do not exceed 3%. The formulas are expressed in terms of six P-wave weak-anisotropy parameters and three Euler angles specifying the orientation of the symmetry planes of the orthorhombic medium. In the case of a dipping reflector, the formulas also depend on the apparent dip angle of the reflector.