  Let $H$ be a Hopf algebra in braided category $\cal C$. Crossed modules over
$H$ are objects with both module and comodule structures satisfying some
comatibility condition. Category ${\cal C}^H_H$ of crossed modules is braided
and is concrete realization of general categorical construction. For quantum
braided group $(H,{\cal R})$ corresponding braided category ${\cal C}^{\cal
R}_H$ of modules is identifyed with full subcategory in ${\cal C}_H^H$.
Connection with crossproducts is discussed. Correct cross product in the class
of quantum braided groups is built. Radford's--Majid's theorem gives equivalent
condition for usual Hopf algebra to be crossproduct. Braided variant and analog
of this theorem for quantum braided qroups are obtained.
