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We develop a novel description of electrically driven vertical-external-cavity surface-emitting semiconductor lasers (VECSELs) mode-locked by saturable absorber mirrors. Our approach is based on an analytical solution of the bidirectional traveling-wave equations for fundamental transverse mode operation. The resulting time-domain equations describe the evolution of the electric fields and carrier-densities at the quantum-well layers of the emitter and absorber structures which are coupled through delayed boundary conditions. For the design considered, we obtain stable mode-locked pulses of few tens of picoseconds at 15-GHz repetition rate in agreement with recently reported experimental results.