We introduce the notion of algebraic fibrant objects in a general model category and establish a (combinatorial) model category structure on algebraic fibrant objects. Based on this construction, we propose algebraic Kan complexes as an algebraic model for infinity-groupoids and algebraic quasi-categories as an algebraic model for (infinity, 1)-categories. We furthermore give an explicit proof of the homotopy hypothesis. (C) 2011 Royal Netherlands Academy of Arts and Sciences. Published by Elsevier B.V. All rights reserved.