Many low-thermal-conductivity (κL) crystals show intriguing temperature (T) dependence of κL: κL∝T-1 (crystal-like) at intermediate temperatures whereas weak T-dependence (glass-like) at high temperatures. It has been in debate whether thermal transport can still be described by phonons at the Ioffe-Regel limit. In this work, we propose that most phonons are still well defined for thermal transport, whereas they carry heat via dual channels: "normal" phonons described by the Boltzmann transport equation theory and "diffuson-like" phonons described by the diffusion theory. Three physics-based criteria are incorporated into first-principles calculations to judge mode-by-mode between the two phonon channels. Case studies on La2Zr2O7 and Tl3VSe4 show that normal phonons dominate low temperatures while diffuson-like phonons dominate high temperatures. Our present dual-phonon theory enlightens the physics of hierarchical phonon transport as approaching the Ioffe-Regel limit, and provides a numerical method that should be practically applicable to many materials with vibrational hierarchy.