We can detect visual movements not only from luminance motion signals (first-order motion) but also from non-luminance motion signals (second-order motion). It has been established for first-order motions that the visual system pools local one-dimensional motion signals across space and orientation to solve the aperture problem and to estimate two-dimensional object motion. In this study, we investigated (i) whether local one-dimensional second-order motion signals are also pooled across space and orientation into a global 2D motion, and if so, (ii) whether the second-order motion signals are pooled independently of, or in cooperation with, first-order motion signals. We measured the direction-discrimination performance and the rating of a global circular translation of four oscillating bars, each defined either by luminance or by a non-luminance attribute, such as flicker and binocular depth. The results showed evidence of motion pooling both when the stimulus consisted only of second-order bars and when it consisted of first-order and second-order bars. We observed global motion pooling across first-order motion and second-order motions even when the first-order motion was not accompanied by trackable position changes. These results suggest the presence of a universal pooling system for first- and second-order one-dimensional motion signals.