A graph is k-linked if for every list of 2k vertices {s 1 , . . . , s k , t 1 , . . . , t k }, there exist internally disjoint paths P 1 , . . . , P k such that each P i is an s i , t i -path. We consider degree conditions and connectivity conditions sufficient to force a graph to be k-linked. Let D(n, k) be the minimum positive integer d such that every n-vertex graph with minimum degree at least d is k-linked and let R(n, k) be the minimum positive integer r such that every n-vertex graph in

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... hich the sum of degrees of each pair of non-adjacent vertices is at least r is k-linked. The main result of the paper is finding the exact values of D(n, k) and R(n, k) for every n and k. Thomas and Wollan [14] used the bound D(n, k) (n + 3k)/2 − 2 to give sufficient conditions for a graph to be k-linked in terms of connectivity. Our bound allows us to modify the Thomas-Wollan proof slightly to show that every 2k-connected graph with average degree at least 12k is k-linked.