Morphometric analysis of meandering channels on the middle and lower Amazon Deep-Sea Fan demonstrates that these channels have definite similarities with meandering subaerial rivers. The relationships between meander wavelength and both channel width and radius of meander curvature for fan channels are similar to those observed for large rivers; however, channel width, depth, and cross-sectional area decrease down a fan channel. Channel slope or gradient, measured along the channel axis, decreases smoothly down fan even though the fan slope (valley slope) which the channel traverses decreases irregularly down fan. Channel sinuosities range from about 1.05 to 2.6 on the fan, and sinuosity along a single channel, especially on the middle fan, appears to increase or decrease locally to compensate for varying fan surface slope (valley slope) to maintain a smoothly decreasing channel slope. This dynamic relationship between valley slope and channel sinuosity suggests that the sinuosities of the Amazon Fan channels have changed (that is, the channels have meandered) to obtain the optimum channel slopes, and the optimum channel slope decreases down fan. It is not possible, however, to determine whether that meandering occurred early in the development of the channel/levee system or throughout its evolution. Down-channel changes in fan and channel slope and maximum flow thickness (combined with variations in flow density) may produce systematic changes in flow characteristics and channel facies down fan.