  Consider the mod 2 homology spectral sequence associated to a cosimplicial
space X. We construct external operations whose target is the spectral sequence
associated to E\Sigma_2 \times_{\Sigma_2} (X\times X). If X is a cosimplicial
E_\infty-space, we couple these external operations with the structure map
E\Sigma_2 \times_{\Sigma_2} (X\times X) \to X to produce internal operations in
the spectral sequence. In the sequel we show that they agree with the usual
Araki-Kudo operations on the abutment H_*(Tot X).
