The relationships between ash-fusion temperature (AFT) and mineral and chemical composition of coals and coal ashes from a wide variety of deposits (41) were studied by a melting test, X-ray diffractometry, light microscopy, differential-thermal, thermogravimetric and chemical analyses. A reliable explanation and prediction of AFT only from the total chemical composition of coal ash is inadequate because most important are the modes of elemental combination (minerals and phases) in coal and coal ash, as well as their behaviour during heating. The coals, which have low-melting temperature ashes, are lower rank coals with increased concentrations of S, Ca, Mg, Fe, and Na and, respectively, sulphates, carbonates, sulphides, oxides, montmorillonite, and feldspars. The coals with high-melting temperature ashes have an advanced rank and increased contents of Si, Al, and Ti and, respectively, quartz, kaolinite, illite, and rutile, as well as some Fe oxides and siderite. The behaviour of chemical components and various coal and coal-ash minerals during heating is discussed, and their refractory and fluxing influence on ash fusibility is described. Lower AFT is related to increased proportions of the fluxing sulphate, silicate and oxide minerals such as anhydrite, acid plagioclases, K feldspars, Ca silicates, and hematite in high-temperature coal ashes. Higher AFT is a result of decreased concentrations of the fluxing minerals and increased concentrations of the refractory minerals such as quartz, metakaolinite, mullite, and rutile in these ashes. Defined softening, hemispherical and fluid ash-fusion temperatures fit various processes of inorganic transformations which are discussed. It is possible to make a reliable explanation and prediction of ash-fusion characteristics when the coal and coal-ash minerals and their amounts, as well as their refractory and fluxing action during heating, are known.