  In this paper we introduce an automorphic variant of the Deligne conjecture
for tensor product of two motives over a quadratic imaginary field. On one
hand, we define some motivic periods and rewrite the Deligne conjecture in
terms of these periods. On the other hand, we define the automorphic analogue
of these motivic periods and then give a purely automorphic variant of the
Deligne conjecture. At last, we introduce some known results of this
automorphic variant.
