Two methods for dissociation of diatomic molecules based on nonperiodic excitation generated by feedback control mechanism are described and analyzed both analytically and by computer simulation. The first method of control design uses nonlinear resonance curve of the system to fulfill the resonance conditions at any time of excitation. The second method is based on the speed-gradient principle. Implementation of the proposed methods by pulse laser control is described. It is shown that both the resonant curve and the speed-gradient algorithms in ideal case (in the feedback loop) ensure dissociation with arbitrarily small intensity of the controlling field from almost all initial conditions. Efficiency of the proposed methods is demonstrated by simulation for example of hydrogen fluoride (HF) molecule dissociation. Simulations confirmed that new methods are more efficient then the existing algorithms based on harmonic (monochromatic) and linear chirping excitation both for the model case of single molecule and for an ensembles of molecules.