The heat transport within living biological tissue is a complicated process coupled with various physiological activities. The nonhomogeneous inner anatomical structure leads to an essential difference from classical heat transfer. The generalized model of bioheat transfer involving the relaxation mechanism as well as nonequilibrium heat transfer is first proposed to explore the heat transport properties within living biological tissues. Due to the volume averaging theory, the new local instantaneous energy equations of blood and tissue are constructed separately by introducing the phase lags, in which the delay effect between the heat flux and temperature gradient absent in existing generalized models is considered. The effective phase lags covering the delay effect and nonequilibrium effect are obtained on this basis. A detailed parametric study has been conducted to estimate the values of these effective phase lags and evaluate their contributions on heat transport within living biological tissues. The results state that the effective phase lags depend on the anatomical structure of tissues and its physical properties. The delay effect is dominated in general and has a higher temperature elevation than that induced by nonequilibrium effect only.