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<p/> <p>The purpose of this paper is to introduce and study two modified hybrid proximal-point algorithms for finding a common element of the solution set <it>EP</it> of a generalized equilibrium problem and the set <inline-formula> <graphic file="1687-1812-2010-590278-i1.gif"/></inline-formula> for two maximal monotone operators <inline-formula> <graphic file="1687-1812-2010-590278-i2.gif"/></inline-formula> and <inline-formula> <graphic file="1687-1812-2010-590278-i3.gif"/></inline-formula> defined on a Banach space <inline-formula> <graphic file="1687-1812-2010-590278-i4.gif"/></inline-formula>. Strong and weak convergence theorems for these two modified hybrid proximal-point algorithms are established.</p>