Abstract
The Hasse principle for similarity is established for restricted classes of skew-hermitian forms over quaternion division algebras with canonical involution and for hermitian forms over division algebras with involution of the second kind. A counterexample is produced to show that the principle cannot hold for skew-hermitian forms over quaternion division algebras in general. This settles the two final cases of Hasse principles for similarity of forms that were missing in the literature.
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