  In this paper, we continue Curto-Hwang-Lee's work to study the connection
between hyponormality and subnormality for block Toeplitz operators acting on
the vector-valued Hardy space of the unit circle.Curto-Hwang-Lee's work focuses
primarily on hyponormality and subnormality of block Toeplitz operators with
rational symbols. By studying the "weak" commutativity, we extend
Curto-Hwang-Lee's result to block Toeplitz operators with symbols of bounded
type.
