Zeolites can be obtained in the process of the alkali-activation of aluminosilicate precursors. Such zeolite–geopolymer hybrid bulk materials merge the advantageous properties of both zeolites and geopolymers. In the present study, the effect of the type and concentration of an activator on the structure and properties of alkali-activated metakaolin, and metahalloysite was assessed. These two different kaolinite clays were obtained by the calcination of kaolin and halloysite, and then activated with sodium hydroxide and water glass. The phase compositions were assessed by X-ray diffraction, the microstructure was observed via scanning electron microscope, and the structural studies were conducted on the basis of the infrared spectra. The structure and properties of the obtained alkali-activated materials depend on both the type of a precursor and the type of an activator. The formation of zeolite phases was observed when the activation was carried out with sodium hydroxide alone, or with a small addition of water glass, regardless of the starting material used. The higher proportion of silicon in the activator solution does not give crystalline phases, but only an amorphous phase. Geopolymers based on metahalloysite have better compressive strength as the result of the better reactivity of metahalloysite compared to metakaolin.