  We analytically study the linear propagation of arbitrarily shaped
light-pulses through an absorbing medium with a narrow transparency-window or
through a resonant amplifying medium. We point out that, under certain general
conditions, the pulse acquires a nearly Gaussian shape, irrespective of its
initial shape and of the spectral profile of the line. We explicitly derive in
this case the pulse parameters, including its skewness responsible for a
deviation of the delay of the pulse maximum from the group delay. We illustrate
our general results by analysing the slow-light experiments having demonstrated
the largest fractional pulse-delays
