A theory of dual pump-probe spectroscopy is developed. At time t appro
ximate to 0 the medium is subjected to two pulses with different carri
er frequencies omega L and omega S. Then the same sample is probed by
two pulses, omega L and omega S, after a delay time t(d). The transmis
sion lineshape is explored as a function of t(d). Time resolution duri
ng one period of the medium vibration can be achieved. The limitation
on the pulse duration t(p) is determined by the dephasing time T-2:t(p
)<<T-2.