Motivated by superstring theories on AdS3, we construct spacetime superconformal algebras (SCAs) living on the AdS3 boundary in terms of the transversal physical degrees of freedom. The SCAs constructed are N=4 large, middle algebras, and N = 3 algebra, corresponding to superstring theories on AdS3 × S × S × S, AdS3 × S × T 4 and AdS3 × (S × S × S)/Z2 backgrounds respectively. e-mail: jingj@itp...