The second order PMD effect on Gaussian pulse propagation in single mode optical fiber is studied. The explicit expression of second order PMD induced pulse distortions is given in the time domain. It is found that the output pulse in each basic state of polarization retains Gaussian shape but some characters such as the frequency chirp and the pulse width have changed. The relationship between these changes and second order PMD is analyzed. The second order PMD influences in 10 Gbit/s and 40 Gbit/s systems are compared. It is found that the tolerable value of second order PMD in 40 Gbit/s systems is one order of magnitude lower than in 10 Gbit/s systems if the pulse broadening must not exceed one tenth of the pulsewidth.