  The q-deformed Fock spaces of higher levels were introduced by
Jimbo-Misra-Miwa-Okado. Uglov defined a canonical bases in q-deformed Fock
spaces of higher levels. Leclerc-Thibon showed a product theorem in q-deformed
Fock spaces of level one. The product theorem is regarded as a formal
$q$-analogue of the tensor product theorem of level one. In this paper, we show
a higher level analogue of Leclerc-Thibon product theorem under a suitable
multi charge condition.
