In this work, the phase-lag concept in the wave theory of heat conduction i
s extended to describe the thermal behavior of anisotropic material. This i
s achieved by assuming that there are phase-lags of different magnitudes be
tween each component of the heat flux vector and the summation of temperatu
re gradients in all directions of the orthogonal coordinate system. Also, e
xpressions are provided to specify the locations of the principal coordinat
e axes, the principal thermal conductivities and the principal thermal rela
xation times.