The loss of contrast sensitivity with eccentricity is well documented, and is steeper for higher spatial frequencies, and for L/M cone-opponent stimuli compared to achromatic or S-cone-opponent. Here, we ask how perceived contrast depends on eccentricity when stimuli are presented at suprathreshold contrasts, and test two opposing predictions. Contrast constancy predicts no loss in perceived contrast across the visual field regardless of changes in detection threshold - appearance depends only on physical contrast. Conversely, perceived contrast may be scaled in the same way as detection threshold, reflecting the proportional increase in stimulus contrast above threshold. We measured perceived contrast for L/M cone-opponent, S-cone opponent, and Ach stimuli up to 18 degrees of eccentricity using a 2AFC contrast matching method between fovea and periphery. We tested a range of reference contrasts from low (close to detection threshold) to high suprathreshold contrasts and we relate suprathreshold perceived contrast to measured detection thresholds. We find evidence for a hybrid model in which apparent contrast is reduced with eccentricity for stimuli in the low and mid contrast range, with contrast constancy only attained at the highest contrasts. When equated for similar sensitivity losses, we find no difference between chromatic and Ach contrast responses.