Alkali-free, aluminium-based accelerators are often used for shotcrete linings in tunnels and mines, where external sulfate attack can occur. Therefore, it is essential to know, if the influence of the accelerators on the cement hydrate assemblage negatively impacts sulfate resistance. This study focuses on the effect of aluminium-based accelerators on cement hydration and the consequences for external sulfate attack. Aluminum sulfate-based accelerators cause rapid setting due to the very early formation of ettringite and accelerate alite hydration. At late ages, significant more AFm phases are formed compared to the reference without accelerator, which during storage in sodium sulfate solution react to ettringite. A significantly higher volume increase due to the formation of additional ettringite during sulfate exposure was calculated by thermodynamic modelling for the accelerated paste compared to the reference. Alkaline accelerators based on sodium aluminate form mainly amorphous calcium (sulfo-) aluminate hydrates at very early age, while ettringite seems to be destabilized. The ettringite quantities formed during storage in sodium sulfate solution are significantly higher than for the reference and the paste with the alkali-free accelerator. This finding compares well to experiments on concrete specimens, where in the mixture with the alkaline accelerator deleterious expansion was observed.