This study focuses on the investigation of compressive strength of geopolymer binders based on alkali-activated ash and slag waste from thermal power plant. It has been found that the significant factors affecting the mechanical strengths are the reactivity of the precursor and curing regimes of geopolymer binders. First of all, the quantity and the structural characteristics of amorphous phases in these materials play a crucial role in determining the mechanical performance. According to the X-ray data, both fly ash and slag as well as the geopolymers based on these precursors, demonstrate the presence of an amorphous hump. The quantity of amorphous phase in slag component (70.4%) is higher than in fly ash one (63.9%). Besides, compared to the original slag, the radius of the first coordination shell for the “low-angle” amorphous phase R1 = 7.3 Å is higher than that of the fly ash R1 = 7.0 Å. This indicates that the slag component demonstrates the presence of regions of increased free volume. On the other hand, the proportion of the crystalline phase in the original slag is 29.6% in comparison with fly ash (36.1%) and is represented primarily by silicon oxide along with minor amount of hematite and magnetite. It has been determined that a sharp decrease in the crystalline phase content with increasing the heating medium temperature and pressure for slag-based geopolymers is observed. The geopolymer obtained by autoclave curing contains only 1.8% crystalline inclusions. DTG analysis indicates that the peaks corresponding to the geopolymers cured under autoclave regimes (both based on fly ash and slag components) are deeper and broader in comparison with binders cured under elevated temperature and atmospheric pressure. The compressive strength of slag-based geopolymer samples is much higher than of ash-based ones regardless of the curing regime. This is due to the properties of slag component: improved reactivity – the higher proportion of amorphous phase and aluminum oxide, lower water demand – the proportion of loss on ignition is practically negligible.