We present simple formulae for qP wave phase velocities in weakly but arbitrarily anisotro-pic media. For their derivation, we use the well-known formula for the first-order perturbation of the qP wave phase velocity, see e.g. Backus (1965). The formula for phase velocity in a generally anisotropic medium corresponds exactly to the one already derived by Sayers (1994). We discuss its sensitivity to the elastic parameters and specify it for special cases of anisotropy frequently encountered in practice. We consider the case of an orthorhombic medium with axes of symmetry coinciding with general coordinate axes, a transversely isotropic medium and a medium with a horizontal axis of hexagonal symmetry. In all the cases, the formulae for the phase velocity contain nondimensional parameters, which represent a generalization of Thomsen's (1986) parameters. The formula for transversely isotropic medium reduces to the well-known formula derived by Thomsen (1986).