Cooperative relaying (CR) is a promising technique to provide spatial diversity by combining multiple signals from source and relay stations. In the present paper, the impact and use of the asymmetric property in hi-directional CR under asymmetric traffic conditions are discussed assuming that CR involves one communication pair and one relay station in a time division duplex (TDD) system. The asymmetric property means that the average communication quality differs for each transmission direction because of the difference in signal power between the combined signals for each direction. First, numerical results show the asymmetric property of hi-directional CR. Next, in order to evaluate the impact of the asymmetric property, the optimal relay position and resource allocation are compared to those in simple multi-hop relaying, which does not have the asymmetric property. Numerical results show that, in order to maximize the overall quality of hi-directional communication, the optimal relay position in CR depends on the offered traffic ratio, which is defined as the traffic ratio of each transmission direction, while the offered traffic ratio does not affect the optimal relay position in multi-hop relaying. Finally, the asymmetric property is used to enhance the overall quality. Specifically, a high overall quality can be achieved by, for example, opportunistically switching to the transmission direction with higher quality. Under asymmetric traffic conditions, weighted proportionally fair scheduling (WPFS), which is proposed in the context of downlink scheduling in a cellular network, is applied to transmission direction switching. Numerical results reveal that WPFS provides a high overall quality and that the quality ratio is similar to the offered traffic ratio.