<p>The paper presents the main lines of a new theory of the seismic dynamics of masonry structures in the context of the masonry Heyman model. The seismic action is represented by a sequence of horizontal acceleration pulses of rectangular shape, alternating in sign, of given intensity and wavelength. The central point of the proposed new theory is the definition of the way in which the dynamical collapse takes place, occurring during the motion of the no-tension structure, excited by the seismic shaking. Two new aspects play a fundamental role in this definition. The first is the configuration of zero strength, in which the potential energy of the weights reaches its maximum and where the structure has completely lost its strength. The second is the occurrence of the gradual accumulation of deformation of the structure that takes place under the pulse sequence, in spite of the alternating pulse action. Collapse thus takes place under the simultaneous achievement of the configuration of zero strength and the arrival of the acceleration pulse that pushes the structure to go beyond this configuration<i>.</i> By increasing the pulse number of the sequence, collapse takes place under smaller values of horizontal acceleration intensity. Finally, an asymptotic sequence of pulses allows an equation to be formulated for the behaviour factor (the ratio of collapse horizontal acceleration intensity to the static acceleration) for safe seismic design.</p>