In a multi-relay system, the instantaneous channel state information (CSI) is usually required at relays to achieve the space diversity. In this paper, we propose a delayed noncoherent relaying scheme to achieve space diversity without requiring knowledge of the instantaneous CSI at the relays. Specifically, each relay will non-coherently amplify and forward its received signals with different delays such that a virtual multipath channel is created between the source and destination. We will first determine the most efficient way to achieve the optimal diversity gain. We will then show that, with spreading or coding, the proposed non-coherent relaying can provide the same diversity order as its coherent counterpart but with a noncoherent penalty. With the simplest spreading scheme, the noncoherent penalty results in a loss of both multiplexing gain and finite-SNR diversity gain. To recover the loss due to this noncoherent penalty, a distributed relay selection algorithm, which can achieve a better outage performance with less energy, is proposed. On the other hand, with the Gaussian-coded noncoherent relaying, no multiplexing gain loss will be incurred but a loss of SNR gain will occur.