A secbnd:ordor'approximation is formulated and studied within the context of the'quasi-particle do.snript.ion of magnetized plasmas. The general case of relatiyisfcic particles in non-uniform but stationary magnetic fields, ami in additional force fields that are strongly non-uniform l)vit.'slowly evolving in time compared with particle gyrations with the cyclotron frequency, is'considered, In order to reveal the physical significance of the second-order approximation, the mean (reduced) particle vHlocdty is calculated up to second order, when polarization particle drift ?? well aB the renomuilizabion of the lower-order 'result become equally,-significant. A general expreHwion for the velocity of particle polarization drift in obtained in terms of quasi particle properties, and with account taken of finite-Larmor- radius ofl'eclK and ndn-vmiformity of magnetic fields. A guiding- centre transformation is found that makes it 'possible to achieve c<]ual lnejui velocities of particle, guiding centre and quaai-particle up to second orcter. Then polarization drifts enter the particle, guiding-centre and quasi-partiele equations of motion.
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