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The theory of the optically pumped passive Cs frequency standard is given. Experimental results confirming qualitatively this theory are presented. The results are also compared to those obtained in the case of Rb. Experimental results on the pressure shift and temperature coefficients of the hyperfine frequency of cesium atoms in four buffer gases, CH4, N2, Ar and Kr are presented. Finally graphs for evaluating a given pressure coefficient and the residual temperature coefficient for mixtures of buffer gases are given.