Prevention of the reaction of sodium and potassium hydroxides with silica [alkali-silica reaction – ASR] in concrete can be shaped by: using non-reactive aggregate, ensuring a low content of sodium and potassium oxides in the concrete mix, or using mineral additives. This article presents the results of research on preventing the ASR reaction in concrete by using mineral additives: pozzolanic and with latent hydraulic properties. The scope of the research included a large group of domestic aggregates with varying degrees of alkaline reactivity. The results of the tests of alkaline expansion of mortars, according to the accelerated method ASTM C 1260-14, allowed us to determine the minimum addition of siliceous fly ash and granulated blast furnace slag, which effectively reduces the expansion of mortars caused by the ASR reaction to the required level below 0.1%. For aggregate with a degree of reactivity R1, with an expansion of 0.1-0.2 %, the addition of 20 % fly ash introduced with Portland ash cement CEM II/A-V effectively eliminates the ASR reaction. For aggregate R1 with an expansion of 0.2-0.3 %, CEM II / B-V Portland ash cement should be used, which contains at least 25 % fly ash. In the case of granulated blast furnace slag, for aggregate R1 with an expansion of 0.1-0.2 %, the minimum amount of additive that effectively eliminates the expansion of mortars caused by the ASR reaction should be 30 %, and for aggregate R1 with an expansion of 0.2-0.3 %, the minimum amount is 50 %. These quantities of granulated blast furnace slag can be fed with CEM II/B-S Portland slag cement and CEM III/A blast furnace cement, respectively.