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This paper contains the more significant part of the article with the sametitle that will appear in the Volume 12 of Journal of Group Theory (2009).  In this paper we determine all algebraic transformation groups $G$, definedover an algebraically closed field $\sf k$, which operate transitively, but notprimitively, on a variety $\Omega$, provided the following conditions arefulfilled. We ask that the (non-effective) action of $G$ on the variety ofblocks is sharply 2-transitive, as well as the action on a block $\Delta$ ofthe normalizer $G_\Delta$. Also we require sharp transitivity on pairs $(X,Y)$of independent points of $\Omega$, i.e. points contained in different blocks.

Algebraic (2,2)-transformation groups