Asymptotic methods are utilized to analyze the propagation of linear, three-dimensional and two-dimensional wave packets in a weakly non-parallel, compressible, zero pressure gradient, boundary layer over a flat plate. Wave packets generated due to a low amplitude coherent perturbation are analyzed in the framework of Linear Stability Theory while omitting the effect of receptivity. Application of two asymptotic techniques, namely the steepest descent method and a Gaussian model are demonstrated. The steepest descent method is used to identify the frequency and spanwise wavenumber of the disturbance wave with the maximum amplitude in the wavepacket at a given location and a Gaussian approximation around these disturbance parameters is used to construct the fine structures of the wavepacket. Details of the wavepacket evolution in boundary layers with edge Mach numbers, Me = 2 and Me = 7 are presented and validity of the asymptotic techniques for these flow conditions are discussed.