A theoretical approach to simulation of the transient spectra in molecular systems with ultrafast photoinduced nonradiative electronic transitions is developed. The evolution of the excited and ground state populations as well as the nonradiative transitions between them are calculated in the framework of the stochastic multichannel point-transition model involving the reorganization of the medium and the intramolecular high frequency vibrational modes. Simulations of transient spectra of donoracceptor pairs excited in the charge-transfer band that are accompanied by ultrafast charge recombination into the ground state demonstrate a possibility of positive band appearance in the transient absorption spectrum caused by those systems in the ground state, which returned there from the excited state. The region of the parameters of the donoracceptor systems where a positive ground state absorption signal can be observed is discussed. A qualitative comparison of the simulated transient spectra with the experimental data on betaine-30 is presented.