The existence of the principal directions of the ground motion based on Arias intensity is well-known. These principal directions do not necessarily coincide with the orientations of recording sensors or with the orientations along which the ground motion parameters such as the peak ground acceleration and the pseudo-spectral acceleration (PSA) are maximum. This is evidenced by the fact that the maximum PSA at different natural vibration periods for horizontal excitations do not correspond to the same orientation. A recent analysis carried out for California earthquake records suggests that an orientation-dependent ground motion measurement for horizontal excitations can be developed. The main objective of this study is to investigate and provide seismic ground motion measurements in the horizontal plane, including bidirectional horizontal ground motions, for Mexican interplate and inslab earthquake records. Extensive statistical analyses of PSA are conducted for the assessment. The analysis results suggest that similar to the case of California records, the average behavior of the ratio of the PSA to the maximum resulting PSA can be approximated by a quarter of an ellipse in one quadrant; and that the ratio can be considered to be independent of the value of the maximum resulting PSA, earthquake magnitude, earthquake distance and the focal depth. Sets of response ratios and attenuation relationships that can be used to represent a bidirectional horizontal ground motion measurement for Mexican interplate and inslab earthquakes were also developed. The existence of the principal directions of the ground motion based on a orientation of the ground motion based on arias intensity is well-known. This is evidenced by the fact that the maximum PSA at different natural vibration periods for horizontal excitations do not correspond to the same orientation. A recent analysis carried out for California earthquake records suggests that an orientation- The main objective of this study is to investigate and provide seismic ground motion measurements in the horizontal plane, including bidirectional horizontal ground motions, for Mexican interplate and inslab earthquake records. Extensive statistical analyzes of PSA are conducted for the assessment. The an alysis results suggest that similar to the case of California records, the average behavior of the ratio of the PSA to the maximum of PSA can be approximated by a quarter of an ellipse in one quadrant; and that the ratio can be considered to be independent the value of the maximum resulting PSA, earthquake magnitude, earthquake distance and the focal depth.