The testing results and physicotechnical properties of next generation concretes with low specific consumption of cement per unit of strength are given. It is shown, that application of fine-grained dry mixes for production of all sorts of next generation concrete: reacting-powder, sand powder-activated and crushed-stone powder-activated, will allow improving the durability of concretes and reducing specific consumption of cement per unit of strength. It is evident that next generation concretes can be not only high strength and super-high strength ones, but also general purpose concretes with the strength performance of Class V15–V40 with specific cement consumption per unit of compression strength equal to 3–5 kg/MPa. To achieve such technical and economic criteria, it is necessary to optimize the composition of rheological matrices in the concrete.