This paper addresses the Coupled Growth in Hypermonotectics experiment carried out aboard NASA's Life and Microgravity Spacelab Mission which took place from June 10 to July 7, 1996. The experiment involved the directional solidification of hypermonotectic (immiscible) alloys in an attempt to obtain steady-state, coupled growth conditions by processing under microgravity conditions. Processing was carried out utilizing the Advanced Gradient Heating Facility directional solidification furnace in order to obtain the high thermal gradients and controlled growth rates required for stability. Solidification under the proper growth conditions was expected to lead to interface stability and the production of a desired aligned fibrous microstructure even for hypermonotectic alloys. The paper covers the objectives of the experiment and a discussion of the anticipated results. While microstructural information is not yet available at the time of writing, results will be presented on the thermal gradients and growth rates obtained and how these compared with predictions.