In this paper we consider the asymptotics of extinction for the nonlinear diffusion reaction equation with non-negative initial data possessing finite support. For ( > 0, both solution and support vanish as t -* T and x -> x 0 . With T as the extinction time we construct the asymptotic solution as T = T -t -• 0 near the extinction point x 0 using matched expansions. Taking x 0 = 0 , we first form an outer expansion valid when r\ -A r r ( m~p ) / 2 ( 1~p ) = 0(1). This is nonuniformly valid for

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... arge \r\\ and has to be replaced by an intermediate expansion valid for \x\ = O(T~1^0) where l 0 is an even integer greater than unity. If p + m > 2 this expansion is uniformly valid while for p + m < 2 , there are regions near the edge of the support where diffusion becomes important. The zero order solution in these inner regions is discussed numerically. ( L 1 ) which become identically zero in finite time, a phenomenon known as extinction of the solution. For initial data with finite support, an essential feature of the solutions to (1.1) is the appearance of interfaces which separate regions