The ultrafast dynamics of electronic and vibrational energy transfer between two- and three-ring linear poly(phenylene ethynylene) units linked by meta-substitution is studied by nonadiabatic molecular dynamics simulations. The molecular dynamics with quantum transitions (1, 2) method is used including an "on the fly" calculation of the potential energy surfaces and electronic couplings. The results show that during the first 40 fs after a vertical photoexcitation to the S(2) state, the nonadiabatic coupling between S(2) and S(1) states causes a fast transfer of the electronic populations. A rapid decrease of the S(1)-S(2) energy gap is observed, reaching a first conical intersection at approximately 5 fs. Therefore, the first hopping events take place, and the S(2) state starts to depopulate. The analysis of the structural and energetic properties of the molecule during the jumps reveals the main role that the ethynylene triple bond plays in the unidirectional energy transfer process.