Abstract: This invention involves a gear transmission mechanism and its device which incorporate double cycloidal equidistant conjugated gear mechanisms and devices, featuring in that a whole branch cyclic cycloidal equidistant curve at a side of the center of curvature of that cycloid is applied with the value of equidistance equal to or smaller than the radius of the rolling circle as the original tooth profile and thus conjugated mutually enveloping cycloidal equidistant curved gear mechanisms with one-tooth-difference, zero-tooth-difference or multi-tooth-difference can be made according to the requirement. Motor pumps and reducers made according to these mechanisms have the advantages of smaller sliding coefficient, smaller pressure angle, greater speed ratio range, lower noise, better strength, higher efficiency, more convenience in machining and lower cost. Therefore these mechanisms can be used to effectively replace the cycloidal lantern gearing with promising development of novel gear transmissions.