Let M be a module. We call a submodule N of M δ-coclosed in M if N has no proper δ-cosmall submodule. Also we call N weak δ-coclosed in M if N has no proper δ-cosmall submodule K with N K singular. In this article, we show that every δ-supplement submodule of M is weak δ-coclosed in M and the converse is true if M is weakly δ-supplemented
