A connected CW-complex $X$ is contractible iff the homotopy groups $\pi_n(X)$ are zero for all $n\geq 1$.
What (if any?) is the analogous statement for the vanishing of all stable homotopy groups $\pi_n^S(X)$ for all $n\geq 1$ ?
More generally, what is (if any?) the analogue of Whitehead's theorem in the stable world?