The addition-agent effect of atoms of alkali metals (K, Na, Li, and Cs) and halogens (Cl and I) introduced into the combustion zone of a dust flame of aluminum particles on the average size of Al2O3 nanoparticles is studied. A physical model of coagulation of a monodisperse aerosol is proposed. The model takes into account the formation of a complex plasma consisting of positive and negative ions, electrons, neutral gas molecules, and suspended particles of the condensed phase in the combustion zone. The effect of the forces of Coulomb repulsion of unipolarly charged Al2O3 particles as well as their possible attraction by ion wind on the constant of the coagulation rate is also taken into account. It is shown that at low ion concentrations in the plasma, the coagulation rate is determined by the Coulomb repulsion of the particles, and at ion concentrations greater than 1020 m−3 the coagulation rate is determined by the attraction of the particles by the ion wind. The results of calculations of the dependence of the average Al2O3 particle size on the concentration of the additives are in a good quantitative agreement with the experimental data. The combined effect of the additives and the equilibrium products of aluminum oxide (AlO, Al, and Al2O) evaporation on the concentration of positive and negative gas ions, electrons, and Al2O3 particle size in the condensation zone is analyzed. The peculiarities of the influence of the additives of electronegative gases (Cl and I atoms) on the coagulation rate of a thermally ionized aerosol and on the particle size of Al2O3 are considered.