A processing arrangement for manufacturing composite cementitious materials, such as hydraulic blended cements, with significantly reduced Portland clinker minerals content. The arrangement includes a milling unit for pregrinding supplementary cementitious materials and highly reactive pozzolans or mineral fillers, such as fly ash, blast furnace slag, fine quartz, granitic quarry fines, and the like, and a milling unit for pregrinding the Portland cement. The pregrinding units are followed by grinding unit for grinding the preground components. The pregrinding units are adapted to work as an open circuit or as a closed circuit for the material being ground.