[en] A Baecklund transformation between two (sets of) differential equations is strong if the transformation equations already imply the two equations. For each dimension n = 2sup(k), k >= 1, the existence of such strong transformations is proved by constructing a wide variety of them. A simple generalization of a known family of Baecklund transformations is also given. One such provides a useful analogy for Yang's 'instanton' equations. (Auth.)