In this paper, some basic theory of "cone quasi-concave multiple Objedive programming" is developed. Tall new class of multiple objective programming problems employs ideas of nondorninated solutions associated with dominance cones. Necessary as well as sufficient conditions for optimal solutions to such problems are provided. Aside from these, in order to find a nondominated solution, we peitiou all the objectives into several mutually exclusive subgroups and assume that the weighted sum of the objectives in each subgroup is quasi-concave for the given weights. This is different from the assumption in the exasting multiple objective programming literature that the weighted sum of all the objective functions is quasiconcave.