A concept of generalized ordered g-quasicontraction is introduced, and some fixed and common fixed point theorems for g-nondecreasing generalized ordered g-quasicontraction mapping in partially ordered complete metric spaces are proved. We also show that the uniqueness of the common fixed point in the case of an generalized ordered g-quasicontraction mapping. Finally, we prove fixed point theorems for mappings satisfying so-called weak contractive conditions in the setting of partially ordered metric space.Presented theorems are generalizations of very recent fixed point theorems due to Golubovic et al.(2012).