  Consider a pseudo-$H$-space $E$ endowed with a separately continuous
biadditive associative multiplication which induces a grading on $E$ with
respect to an abelian group $G$. We call such a space a graded pseudo-$H$-ring
and we show that it has the form $E = cl(U + \sum_j I_j)$ with $U$ a closed
subspace of $E_1$ (the summand associated to the unit element in $G$), and any
$I_j$ runs over a well described closed graded ideal of $E$, satisfying $I_jI_k
= 0$ if $j \neq k$. We also give a context in which graded simplicity of $E$ is
characterized. Moreover, the second Wedderburn-type theorem is given for
certain graded pseudo-$H$-rings.
