The derivation of the governing equations for modal aerosol dynamics (MAD) models is presented. MAD models represent the aerosol size distribution as an assemblage of distinct populations of aerosol, where each population is distinguished by size or chemical composition. The size distribution of each population is approximated by an analytical modal distribution function; usually by a lognormal distribution function. By substituting the MAD representation of aerosol size distributions into the governing equation for aerosol processes, the governing differential equations for MAD models are derived. These differential equations express the time dependence of the moments of the aerosol size distribution and are called Moment Dynamics Equations (MDEs). The MDEs for Continuously-Stirred Tank Aerosol Reactors (CSTARs) are also derived.