Almost all existing analysis methods for building ventilation airflows, such as the simpleanalytical methods, multi-zone methods and computational fluid dynamics (CFD), give onlyone unique solution for one set of identical input parameters when started with zeroinitialization or zero initial conditions. This can be shown to be incorrect in some situations.Multiple stable solutions are found in some very simple buildings, which indicate that thebuilding airflows are of a nonlinear dynamical system. As a nonlinear dynamical system, airand smoke flows in buildings can be very sensitive to perturbations and/or initial conditions.Dynamical nonlinear phenomena can be of great significance for indoor air quality, heattransfer, and smoke transport in buildings, in particular in naturally and hybrid ventilatedbuildings. A number of examples are given in this paper to illustrate the situations wheremultiple steady solutions exist. Practical recommendations are suggested in terms of designand analysis based upon the current understanding.