In this paper, a resource management for fixed relay stations (FRS) with the limited capability is considered in downlink OFDMA multi-hop cellular networks. All of MSs which want to use a FRS in multi-hop transmission can not be supported when the capability of the FRS is insufficient. Hence, the multi-hop user admission (MUA) is required to determine the admitted MSs to use the FRS because the gain obtained from multi-hop transmission is different to each MS. The problem of MUA is formulated to maximize the total multi-hop gain which the FRS can achieve from the admitted MSs, and this problem is proven to be NP-hard. Hence, two efficient heuristic algorithms for MUA are proposed. One is the balanced link-MUA (BL-MUA) algorithm which gives priorities of admission with attaching importance to the load balance between the BS-FRS link and the FRS-MS link. The other is the focused link-MUA (FL-MUA) algorithm which considers only the load state of the FRS-MS link in admission. Through the numerical results, it is verified that the FL-MUA algorithm obtains similar performance to the BL-MUA algorithm with less complex-ity. In addition, the total number of saved subcarriers in a FRS increases and more MSs can be supported in a cell with low blocking probability by the proposed algorithms.