A Raman-Ramsey Cs cell atomic clock is presented. The relaxation times of the population and the hyperfine coherences in the cell are measured. The effect on the central Ramsey fringe amplitude of the critical experimental parameters such as laser intensity, magnetic field, temperature, and Ramsey time is investigated. The existence and impact of the additional Deltam = 2 transitions involved in the pumping scheme are pointed out. Narrow resonance linewidths as low as 33 Hz with reasonable signal-to-noise ratios have been recorded. By removing a frequency drift attributed to the cell, the achieved frequency stability is 7 times 10-13 tau-1/2. The main noise contributions that limit the short-term frequency stability are reviewed and estimated.