Abstract: In this paper Prony method is extended to the processing of data with white and/or colored noise. When the observed noise is white, the observation procedure is obeyed the auto-regressive moving-average model in which the autoregressive coefficients are equalled to the moving-average coefficients, and two kinds of modified Yule-Walker normal equations, which yieled the unbiased estimates of autoregressive coefficients, are derived. For the colored observed noise, new concept of second regression is developed, through which the colored noise can be whitened. Finally, the theoretical results are checked by the simulative calculations on a computer.