It was intended in this research to detect and to analyze the existence of conditional volatility in the time series of the prices of the spot market of the Brazilian coffee in the New York Board of Trade (NYBOT) in the period between January of 1946 and December of 2000. The results of the models of GARCH type, applied for the prices of the coffee, indicated that the conditional variance of the residues of the models possess unit roots and the same one will not present a behavior of reversion to its historical average with passing of the time, after a shock. This happens because, the coefficients of volatility persistence had been all bigger or next to one