We consider design of asynchronous orthogonal frequency division multiplexing (OFDM) based diamond two-way-relay (DTWR) systems in a time-varying frequency-selective (doubly-selective) fading channel. In a DTWR system, two users exchange their messages with the help of two relays. Most of the existing works on asynchronous DTWR systems assume only small relative propagation delays between the received signals at each node that do not exceed the length of the cyclic-prefix (CP). However, in certain practical communication systems, significant differences in delays may take place, and hence existing solutions requiring excessively long CPs may be highly inefficient. In this paper, we propose a delay-independent CP insertion mechanism in which the CP length depends only on the number of subcarriers and the maximum delay spread of the corresponding channels. We also propose a symbol detection algorithm that is able to tolerate very long relative delays, that even exceed the length of the OFDM block itself, without a large increase in complexity. The proposed system is shown to significantly outperform other alternatives in the literature through a number of specific examples. © 2015 IEEE.