Let S be a set of n points in a metric space, and let k be a positive integer. Algorithms are given that construct k ‐fault‐tolerant spanners for S . If in such a spanner at most k vertices and/ or edges are removed, then each pair of points in the remaining graph is still connected by a “short” path. First, an algorithm is given that transforms an arbitrary spanner into a k ‐fault‐tolerant spanner. For the Euclidean metric in R
d
, this leads to an O(n log n + c
k
n) ‐time algorithm that constructs a k ‐fault‐tolerant spanner of degree O(c
k
) , whose total edge length is O(c
k
) times the weight of a minimum spanning tree of S , for some constant c . For constant values of k , this result is optimal. In the second part of the paper, algorithms are presented for the Euclidean metric in R
d
. These algorithms construct (i) in O(n log n + k
2
n) time, a k ‐fault‐tolerant spanner with O(k
2
n) edges, and (ii) in O(k n log n) time, such a spanner with O(k n log n) edges.
