An optical design for an astronomical adaptive optics system using two deformable mirrors is presented. The design is intended to test the principles of multiconjugate adaptive optics. Multiconjugate adaptive optics is a technique which uses multiple deformable mirrors placed in the system so that they are optically conjugate to different altitudes in the atmosphere. The purpose of the multiple deformable mirrors is to enlarge the isoplanatic angle for the adaptive optics system. The principle of adaptive optics and the current work in multiconjugate optics are reviewed in this thesis. The optical design was made to be used at the F/8 Cassegrain focus of the 3.58m Canada-France-Hawaii telescope. The design has two deformable mirrors, a SCIDAR camera, a natural guide star wavefront sensor, four laser guide star wavefront sensors, and an atmospheric dispersion corrector. The system field of view is 22 arcseconds with the four laser guide stars placed at 37 arcseconds from the center of the field. The ranges of altitude which the deformable mirrors can be placed optically conjugate to are: 0 km to 7.2 km for the lower deformable mirror, and 1.8 km to 9 km for the upper deformable mirror, with a minimum conjugate distance of 1.8 km between the mirrors. The image quality at the science camera is better than a Strehl ratio of 0.93 over the whole field of view with the effects of atmospheric dispersion being corrected by an atmospheric dispersion corrector.