A process for the preparation of cellular plastics, preferably hard structural polyurethane foams, by the polyisocyanate polyaddition process involves reacting a) an organic and/or modified organic polyisocyanate with b) at least one high-molecular-weight compound containing at least two reactive hydrogen atoms and, if desired, c) a low-molecular-weight chain extender and/or crosslinking agent, in the presence of d) a blowing agent from the group comprising tertiary alcohols (di), preferably tertiary butanol, or a mixture of at least one tertiary alcohol (di) and water (dii), e) a catalyst and, if desired, f) assistants and/or additives.