Based on the extended Huygens–Fresnel integral, we derivedjkljfk a propagation law for the generalized stokes parameters of a stochastic electromagnetic TAGSM beam propagating in turbulent atmosphere by use of tensor method, and use the Stokes parameters to investigate properties of the Stokes parameters, the scintillation indexes of Stokes parameters, the state of polarization (including the spectral degree of polarization, the orientation angle the degree of ellipticity) of elliptically polarized electromagnetic TAGSM beams. It is found that, after propagating through a turbulent atmosphere, the stokes parameters, the scintillation indexes of Stokes parameters and the state of polarization of electromagnetic TAGSM beams will change on propagation and this changes is dependent upon the atmospheric turbulence and the parameters of the source beams.