Based on the theory of FREDRIKSSON (1963) an attempt is made to understand the origin of chondrules by studying examples from the meteorites of Tieschitz, Lanzenkirchen, and Mezö-Madaras. Investigations by means of an electron probe microanalyzer, and structural considerations, lead to the following conclusions: 1. The chondrules are of magmatic origin;2. The crystallization took place from a strongly undercooled melt; 3. Many chondrules in the meteorites of Tieschitz and Mezö-Madaras started to crystallize in the liquidus-solidus field of the respective primary phase, thus leading to a marked disequilibrium; 4. The crystallization of the primary phases of the chondrules of the meteorite of Lanzen-kirchen and some of the chondrules of the meteorites of Mezö-Madaras and Tieschitz did not start until the subsolidus region was reached; 5. This process led to true coexistent phases, i.e. those phases which crystallized simultaneously are in a true equilibrium, despite their crystallization from an extreme disequilibrium; 6. The structural relationship of phenocrysts and the matrix in many chondrules is a disequilibrium structure, even in so-called "equilibrium" chondrites. The consequences concerning the origin of the chondrules are indicated tentatively.