Plaids are ambiguous stimuli that can be perceived either as a coherent pattern moving rigidly or as two gratings sliding over each other. Here we report a new factor that affects the relative strength of coherency versus transparency: the global direction of motion of the plaid. Plaids moving in oblique directions are perceived as sliding more frequently than plaids moving in cardinal directions. We term this the oblique plaid effect. There is also a difference between the two cardinal directions: for most observers, plaids moving in horizontal directions cohere more than plaids moving in vertical directions. Two measures were used to quantify the relative strength of coherency vs. transparency: C/[C+T] and RTtransp. Those measures were derived from dynamics data obtained in long-duration trials (>1 min) where observers continually indicated their percept. The perception of plaids is bi-stable: over time it alternates between coherency and transparency, and the dynamics data reveal the relative strength of the two interpretations [Vision Research 43 (2003) 531]. C/[C+T] is the relative cumulative time spent perceiving coherency; RTtransp is the time between stimulus onset and the first report of transparency. The dynamics-based measures quantify the relative strength of coherency over a wider range of parameters than brief-presentation 2AFC methods, and exposed an oblique plaid effect in the entire range tested. There was no interaction between the effect of the global direction of motion and the effect of gratings' orientations. Thus, the oblique plaid effect is due to anisotropies inherent to motion mechanisms, not a bi-product of orientation anisotropies. The strong effect of a plaid's global direction on its tendency to cohere imposes new and important constraints on models of motion integration and transparency. Models that rely solely on relative differences in directions and/or orientations in the stimulus cannot predict our results. Instead, models should take into account anisotropies in the neuronal populations that represent the coherent percept (integrated motion) and those that represent the transparent percept (segmented motion). Furthermore, the oblique plaid effect could be used to test whether neuronal populations supposed to be involved in plaid perception display tuning biases in favor of cardinal directions.