The purpose of this paper is to test the contemporary concept of biological species against some of the problems caused by treating species as spatiotemporally extended entities governed by criteria of persistence, identity, etc. After outlining the general problem of symmetric division in natural objects, I set out some useful distinctions (section 1) and confirm that species are not natural kinds (section 2). Section 3 takes up the separate issue of species definition, focusing on the Biological Species Concept (BSC). Sections (...) 4 and 5 examine the matter of species identity over space and time respectively, as determined by the BSC. Both gradualistic and punctuated equilibrium models of speciation are discussed. In section 6 I argue that the BSC fails to determine adequate criteria for dealing with certain kinds of speciation. Section 7 moves speculatively beyond the BSC to a brief examination of alternatives. (shrink)