The potential alkali-silica reactivity (ASR) of various combinations of Portland-composite cements CEM II/A, and Lithuanian aggregates from three gravel deposits are investigated in this work. These aggregates which contain about (2 - 4 %) reactive siliceous rocks (mostly rapid reacting opal and slower reacting flint) could possibly be assigned to Class II-S (potentially alkali-reactive). Two indicators were used to assess the effectiveness of the supplementary cementing materials (SCMs) – slag (S), fly ash (FA) and burnt shale, which are present up to 20 % in the cement: the expansion of the mortar specimens in a hot alkali solution and the intensity of the ASR-caused surface damage in the warm humid environment (60 °C and 100 % RH). The presence of S (~15 %) and FA (10 %, 15 %, 20 %) in the cements decreases the expansion, but no mitigating effect (in the case of S) or even a stimulating effect (in the case of 10 % and 15 % FA) was observed for the ASR-caused surface damage, the effect only occurred in the case of the threshold content (20 %) of FA in the cement. The stimulating effect of burnt shale (~ 18 %) was observed on both the expansion and surface damage. A strong linear correlation (R = 0.95) between the changes in the flexural strength and expansion was observed in the 28-day specimens when tested according to AAR-2.2. © 2019 University of Chemistry and Technology. All rights reserved.