The k-set agreement problem is a generalization of the consensus problem where processes can decide up to k different values. Very few papers have tackled this problem in dynamic networks, and to the best of our knowledge, every algorithm proposed so far for k-set agreement in dynamic networks assumed synchronous communications. Exploiting the formalism of the Time-Varying Graph model, this paper proposes a new failure detector Sigma-bottom-k, based on Sigma-k and Sigma-bottom, for solving k-set agreement in asynchronous dynamic networks. We present two algorithms that implement this new failure detector, making assumptions on the number of process failures and graph connectivity. We also provide an algorithm for solving k-set agreement using Sigma-bottom-z , under an assumption on the relative values of k and z.