[1] We discuss properties of extremely low-frequency (ELF) and very low-frequency (VLF) electromagnetic waves in the Earth's magnetosphere. General expressions for wave magnetic field polarization and for the angle  P between the direction of the Poynting flux vector and the ambient magnetic field are derived for low-amplitude (linear) waves taking into account first-order finite gyroradius effects. The wave magnetic field is always in a plane perpendicular to the direction of the wave propagation, and the polarization depends on wave frequency (or wavelength), dispersion, and plasma parameters. In a warm plasma, the Poynting flux is not aligned with the group velocity and generally deviates from the wave propagation direction, except for parallel propagation. Numerical estimates for  P and wave polarization are made for plasmaspheric hiss (at L = 2, 4, and 6) for typical plasma parameters and for the case of elevated electron temperature (5 keV). The plasmaspheric hiss wave magnetic field is right-hand circularly polarized, except for highly oblique hiss waves which are elliptically polarized. We note a possible transition to the magnetosonic wave regime at short wavelengths. The maximum Poynting flux angle is 20 ı . Estimates for daytime outer zone chorus (L = 6) show two regions of oblique Poynting flux corresponding to a low-frequency band (! < ! ce /2) and to a high-frequency band (! ce /2 < ! < ! ce ) where ! and ! ce are the wave frequency and the electron cyclotron frequency, respectively. The wave magnetic field polarization varies from circular to elliptical at shorter wavelengths. In a hot plasma, chorus is elliptically polarized. The maximum  P in the low-frequency band is 20 ı .  P can reach 60 ı in the high-frequency band. Our results are consistent with the Poynting flux statistics of Polar measurements.Citation: Verkhoglyadova, O. P., B. T. Tsurutani, and G. S. Lakhina (2013), Theoretical analysis of Poynting flux and polarization for ELF-VLF electromagnetic waves in the Earth's magnetosphere,