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In this work, we employ multiple energy harvesting relays to assist information transmission from a multi-antenna hybrid access point (HAP) to a receiver. All the relays are wirelessly powered by the HAP in the power-splitting (PS) protocol. We introduce the novel concept of hybrid relay communications, which allows each relay to switch between two radio modes, i.e., the active RF communications and the passive backscatter communications, according to its channel and energy conditions. We envision that the complement transmissions in two radio modes can be exploited to improve the overall relay performance. As such, we aim to jointly optimize the HAP's beamforming, individual relays' radio mode, the PS ratio, and the relays' collaborative beamforming to enhance the throughput performance at the receiver. The resulting formulation becomes a combinatorial and non-convex problem. Thus, we firstly propose a convex approximation to the original problem, which serves as a lower bound of the relay performance. Then, we design an iterative algorithm that decomposes the binary relay mode optimization from the other operating parameters. In the inner loop of the algorithm, we exploit the structural properties to optimize the relay performance with the fixed relay mode in the alternating optimization framework. In the outer loop, different performance metrics are derived to guide the search for a set of passive relays to further improve the relay performance. Simulation results verify that the hybrid relaying communications can achieve 20% performance improvement compared to the conventional relay communications with all active relays.