In this paper we firstly construct the category $\mathbf{CRPOS}^{ep}_\mathcal{R}$ with objects the same as $\mathbf{CRPOS}_\mathcal{R}$(with as objects$\mathcal{R}-$complete $\mathcal{R}-$posets where$\mathcal{R}-$limits preserve orders of approximating order family and as morphisms $\mathcal{R}-$continuous mappings) and as morphismse-p pairs. Secondly $\omega-$chains, $\mathcal{R}-$chains and$\mathcal{R}-$completeness are defined in$\mathbf{CRPOS}^{ep}_\mathcal{R}$. They are generalizations of$\omega-$chains and $\omega-$completeness in poset. Thirdly we give a kind of characterizations of $\mathcal{R}-$limit in$\mathbf{CRPOS}^{ep}_\mathcal{R}$. Finally we prove that $\mathbf{CRPOS}^{ep}_\mathcal{R}$ is $\mathcal{R}-$complete. It is worth pointing out that a $\mathcal{R}-$limit construction in$\mathbf{CRPOS}^{ep}_\mathcal{R}$ is given in this work.