We present algorithms for computing small stretch spanners in the streaming model. An (alpha,beta)-spanner of a graph G is a subgraph S of G such that for each pair of vertices the distance in S is at most alpha times the distance in G plus beta. We assume that the graph is given as a stream of edges and vertices, and that only one pass over the data is allowed. Furthermore, the number of vertices and edges are not known in advance. We denote by m the current number of scanned edges and by n the current number of discovered vertices.

In this model we show how to compute a (k,k-1)-spanner of an unweigthed undirected graph, for k=2,3, in O(1) amortized processing time per edge/vertex. The computed (k,k-1)-spanners have O(n^{1+1/k}) edges and our algorithms use only O(n^{1+1/k}) words of memory space. In case only Theta(n) internal memory is available, the same spanners can be  computed using O(n^{1+1/k}/B) external memory blocks, each of size B. Each edge/vertex is processed in O(1) amortized time plus O(1/B) amortized block transfers.