Abstract.It is proved that the following spaces are absolute retracts: every F-space with a Schauder basis and certain function spaces along with their subgroups of integer-valued elements. It is also observed that for every o-compact convex set, the absolute extension property for compacta implies the AR-property.1. Introduction. The purpose of this paper is to provide new examples of infinite-dimensional ANRs. Detecting the ANR-property of convex subsets of nonlocally convex metric linear spaces and topological groups is of great importance. For example, the topological classification of these spaces, given recently in [4, 5 and 3], required the ANR-property. We prove that the following spaces are absolute retracts: (1) every complete metric linear space (= F-space) with a Schauder basis, (2) certain function spaces which include Lp (p 5= 0) and Orlicz spaces, and (3) additive subgroups consisting of all integer-valued functions in certain function spaces. Consequently, each of these spaces, when complete and separable, is homeomorphic to a Hubert space [4, 5]. The argument used in verifying the AR-property of the above examples is also employed to show that the AR and the AE(fé') (absolute extension property for compacta) properties coincide for a-compact convex sets. This enables us to find a dense convex topological copy of 2, the linear span of the Hilbert cube in the Hilbert space l2, in every separable infinite-dimensional complete convex set.Our approach is very elementary and mostly involves the natural equiconnected structures of convex sets and contractible groups. We also employ the admissibility