Abstract: The multiple-access relay channel is a model where multiple sources communicate with a single destination in the presence of a relay node. Simultaneously, we also consider that each source receive message (namely generalized feedback) from the other source. Examples of such networks include hybrid wireless sensor and multi-hop networks, where cooperation between the nodes is either undesirable or not possible, but one can use a relay node to aid communication between the sources and the destination. Achievable rate regions for the discrete memoryless multiple access relay channel with generalized feedbacks were derived and it can be also extended to Gaussian channels. Coding scheme based on rate splitting and decode-forward strategies was proposed. Cooperations between the two sources and between source and relay via block Markov superposition encoding enhance communication efficiency. Regular encoding and backward decoding were also included in this new coding scheme. The results show that the derived achievable region results are more general than previously known results including them as special cases. Furthermore over Gaussian channels, achievable region is expanded.