Alcalde is the traditional Spanish municipal magistrate, who had both judicial and administrative functions. An alcalde was, in the absence of a corregidor, the presiding officer of the Castilian cabildo and judge of first instance of a town. Alcaldes were elected annually, without the right to reelection for two or three years, by the regidores of the municipal council. The office of the alcalde was signified by a staff of office, which they were to take with them when doing their business. A woman who holds the office is termed an Alcaldesa.
Mayan alcaldes from Guatemala, 1891
A cabildo or ayuntamiento was a Spanish colonial and early postcolonial administrative council that governed a municipality. Cabildos were sometimes appointed, sometimes elected, but were considered to be representative of all land-owning heads of household (vecinos). The colonial cabildo was essentially the same as the one that was developed in medieval Castile.
1810 meeting of the cabildo in Buenos Aires
Depiction of the main cabildo buildings of the Viceroyalty of the Río de la Plata.
Cabildo of Salta, Argentina.
Vargas, José María; Cevallos García, Gabriel and others investigators. (1985)