The critical point, CP (T, P), of the phase diagram quantifies the minimum amount of kinetic energy needed to prevent a substance from existing in a condensed phase. Therefore, the CP is closely related to the properties of the fluid far below the critical temperature. Approaches designed to predict thermophysical properties of a system necessarily aim to provide reliable estimates of the CP. Vice versa, CP estimation is impossible without knowledge of the vapor phase behavior. We report ab initio Born-Oppenheimer molecular dynamics (BOMD) simulations of sodium and potassium chlorides, NaCl and KCl, at and above their expected CPs. We advance the present knowledge regarding the existence of ionic species in the vapor phase by establishing significant percentages of atomic clusters: 29-30% in NaCl and 34-38% in KCl. A neutral pair of counterions is the most abundant cluster in the ionic vapors (ca. 35% of all vaporized ions exist in this form). Unexpectedly, an appreciable fraction of clusters is charged. The ionic vapor composition is determined by the vapor density, rather than the nature of the alkali ion. The previously suggested CPs of NaCl and KCl appear overestimated, based on the present simulations. The reported results offer essential insights into the ionic fluid properties and assist in development of thermodynamic theories. The ab initio BOMD method has been applied to investigate the vapor phase composition of an ionic fluid for the first time.