Approximate formulae for the qP wave phase velocity, polarization vector and normal moveout in an arbitrary weakly anisotropic medium are presented. They are all expressed in terms of parameters, which represent a natural generalization of parameters introduced by Thomsen (1986). The formulae and the parameters have properties of Thomsen's (1986) formulae and parameters: (i) the approximate equations are considerably simpler than exact equations for qP waves; (ii) the generalized parameters are nondimensional quantities; (iii) in the limiting case of weakly anisotropic media, in isotropic media, the generalized parameters reduce to zero and the corresponding equations reduce to equations for isotropic media; (iv) the generalized parameters are linearly related to the density normalized elastic parameters. For the case of transverse isotropy, the equations and the generalized parameters reduce to equations and parameters of Thomsen (1986). Accuracy of presented formulae is illustrated on two examples of a hexagonally symmetric material with a horizontal axis of symmetry, one with qP wave anisotropy less than 1%, the other one with anisotropy of about 20%. Even for the latter material, satisfactory results are obtained.