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Mobile devices equipped with multiple network interfaces can increase their throughput by making use of parallel transmissions over multiple paths and bandwidth aggregation, enabled by the stream control transport protocol (SCTP). However, the different bandwidth and delay of the multiple paths will determine data to be received out of order and in the absence of related mechanisms to correct this, serious application-level performance degradations will occur. This paper proposes a novel quality-aware adaptive concurrent multipath transfer solution (CMT-QA) that utilizes SCTP for FTP-like data transmission and real-time video delivery in wireless heterogeneous networks. CMT-QA monitors and analyses regularly each path's data handling capability and makes data delivery adaptation decisions to select the qualified paths for concurrent data transfer. CMT-QA includes a series of mechanisms to distribute data chunks over multiple paths intelligently and control the data traffic rate of each path independently. CMT-QA's goal is to mitigate the out-of-order data reception by reducing the reordering delay and unnecessary fast retransmissions. CMT-QA can effectively differentiate between different types of packet loss to avoid unreasonable congestion window adjustments for retransmissions. Simulations show how CMT-QA outperforms existing solutions in terms of performance and quality of service.