The propagation of strong femtosecond laser pulses,which have characteristics of high-power,short pulse-width and wide spectrum,involves many linear and nonlinear effects.So,higher-order effects have important impacts on the propagation.The nonlinear propagation equation with the delayed Raman Kerr response is solved numerically.In the article,the properties of nonlinear refractive index,self-focusing and spectrum broadening due to Raman delayed Kerr nonlinearity of strong femtosecond pulses propagating in atmosphere are studied.The pulse width is as short as tens of femtosecond,or as almost the Raman delayed Kerr response time.The numerical results show that Raman delayed Kerr nonlinearity lowers the maximal nonlinear refractive index,moves the peak value to the tail part of the pulse.These phenomenon become more obvious with the increase of Raman delayed Kerr nonlinearity.And it makes the distribution of on-axis intensity asymmetrical.The self-focusing occurs firstly in the trailing part of the pulse,which weakens the effect of self-focusing.Raman delayed Kerr nonlinearity also generates more frequency shifts to long wave than to short wave,which produces a red-shift to the center of broadening spectrum.The simulation results also indicate that the shorter the initial pulse width,the larger impact of Raman delayed response to the propagation.