  We extend the formalism of the relativistic thermal and kinematical
Sunyaev-Zeldovich effects to the observer's system (the Solar System) moving
with a velocity $\beta_{S}$ with respect to the cosmic microwave background
radiation. We confirm the results recently obtained by Chluba, Huetsi, and
Sunyaev in the lowest order of the observer's velocity $\beta_{S}. We give a
more general analytic expression for the thermal and kinematical
Sunyaev-Zeldovich effects corresponding to the observer's system with the power
series expansion approximation in terms of $\theta_{e}$. It is found that the
effect of the motion of the observer on the Sunyaev-Zeldovich effect will
become important in the future high precision observation projects of the
Sunyaev-Zeldovich effect.
