  The paper proves two results involving a pair (A,B) of P-biisometric or
(m,P)-biisometric Hilbert-space operators for arbitrary positive integer m and
positive operator P. It is shown that if A and B are power bounded and the pair
(A,B) is (m,P)-biisometric for some m, then it is a P-biisometric pair. The
important case when P is invertible is treated in detail. It is also shown that
if (A,B) is P-biisometric, then there are biorthogonal sequences with respect
to the inner product <.;.>_P=<P.;.> that have a shift-like behaviour with
respect to this inner product.
