  Ind-varieties of generalized flags have been studied for two decades.
However, a precise statement of when two such ind-varieties, one or both being
possibly ind-varieties of isotropic generalized flags, are isomorphic, has been
missing in the literature. Using some recent results on the structure of
ind-varieties of generalized flags, we establish a criterion for the existence
of an isomorphism as above. Our result claims that, with only two exceptions,
isomorphisms of ind-varieties of generalized flags are induced by isomorphisms
of respective generalized flags. The exceptional isomorphisms correlate with a
well-known result of A. Onishchik from 1963.
