Abstract. In this paper, we introduce the weakly monotone Preˇsi´c typemappings in product spaces when the underlying space is an ordered conemetric space. Some fixed point results for such mappings are also provedwhich generalize and unifyseveral known results in metric and cone metricspaces with normal cone. The results are supported by examples. 1. IntroductionIn 1905, the famous French mathematician Fr´echet [4] introduced the con-cept of a metric space. According to the need, several mathematicians gen-eralized this concept in various directions. In 1934, a Serbian mathematicianKurepa [10, 11] introduced more abstract metric spaces, in which the metrictakes values in an ordered vector space. For some more similar generalizationsthe reader is referred to [12, 23, 29].Recently, Huang and Zhang [6] reintroduced such spaces under the name ofcone metric spaces, where every pair of elements is assigned to an element of aBanach space equipped with a cone which induces a natural partial order. Inthe same work, they investigated the convergence in cone metric spaces, intro-duced the notion of their completeness, and proved some fixed point theoremsfor mappings satisfying various contractive conditions on these spaces.On the other hand, when considering the convergence of some particular se-quences, Preˇsi´c [20] generalized the Banach contraction principle [1] in productspaces and proved the following theorem.Theorem 1.1. Let (X,d) be a complete metric space, ka positive integer andT: X