This thesis examines the phenomenon of structural instability from second-order effects (P-Delta effects) in structures subjected to seismic excitations. A necessary condition for instability during the response to a strong earthquake is that, at a certain point in time, the lowest eigenvalue of the effective stiffness becomes negative. This is equivalent to stating that the effective tangent stiffness, in these instants, is not positive definite. Design constraints in multistory structures are such that the lowest eigenvalue of the second-order elastic stiffness is large when the behavior is elastic. During intense ground motion, however, plasticity develops and the associated loss of stiffness, depending on the spatial distribution, can lead to configurations that are statically unstable.