A process for the flotation of non-sulfidic minerals or ores, is disclosed in which crushed crude minerals or ores are mixed with water and a collector to form a suspension, air is introduced into the suspension in the presence of a reagent system, and a floated foam containing the non-sulfidic mineral or ores is formed therein along with a flotation residue comprising the gangue polymeric esterquats as the collector polymeric esterquats. The polymeric esterquats are obtained by reacting alkanolamines with a mixture of monocarboxylic acids and dicarboxylic acids and quaternizing the resulting esters, optionally after alkoxylation.