Femtosecond soliton propagation in fibers with slowly decreasing dispersion(FSDD ) has been investigated by solving numerically the generalized nonlinearSchrodinger equation which includes the contributions of Kerr and Raman third ordernonlinearity. A pulse-width stabilized femtosecond pulse is discovered and described as aresult of the combined action of the third-order dispersion and Raman self-scatteringeffects. We also find that the third-order dispersion effect has much more important rolesin femtoseco