We have studied the absorption spectrum of a displaced distorted oscillator molecular system where the lower electronic state is in thermal equilibrium. In this occasion a method is devised to calculate the Franck-Condon factor through the use of displacement and squeezing operators. The relative rate of single vibronic level transitions from an excited electronic state to another excited electronic state is also studied. In both the cases the relevant effect of temperature, displacement and ratio of curvatures of the potential surfaces are investigated. The state-to-state transition in multimode system is analyzed in regard to the influence of energy gap and above parameters. (C) 2002 Elsevier Science B.V. All rights reserved.