Abstract: The cementitious material comprises an initial mixture of portland cement clinker and a modifier ranging in weight from approximately 0.5% to 5%, preferably 1%, of the weight of the clinker. The modifier is selected from a group comprising (a) a melamine formaldehyde-sodium bisulfite copolymer, and (b) sodium naphthalene sulfonate. The portland cement clinker and the modifier are intimately mixed and caused to react together in a solid state reaction by energetically grinding them together in a highly energetic ball-and-tube grinding mill to a high degree of fineness of at least approximately 5000 Blaine. Modified cementitious materials are produced by providing an additional constituent in the initial mixture comprising a hard, dense, substantially inert mineral material ranging up to 70% of the mixture by weight. The percentages of the portland cement clinker and the modifier are correspondingly reduced. The modified initial mixture is ground as before.