Fixed point results are presented for single-valued cyclic weakly phi_F-contractive mappings on complete metric spaces (X; d), where phi: [0;+1)--> [0;+1) is a function with phi^{-1}(0) = {0}, phi(t) < t for all t > 0 and phi(t_n)-->0 implies t_n--> 0, and F : [0;+1) ! [0;+1) is continuous with F^{-1}(0) = {0} and F(t_n)-->0 implies t_n-->0. Our results extend previous results given by Rhoades (2001)[20], Moradi and Beiranvand (2010)[13], Amini-Harandi (2010)[2] and Karapinar (2011)[11].