In the present paper, we characterize $(r^q(u,p):f_\infty)$, $(r^q(u,p):f)$ and $(r^q(u,p):f_0)$; where $f_\infty$, $f$ and $f_0$ denotes, respectively, the spaces of almost bounded sequences, almost convergent sequences and almost sequences converging to zero, where the space $r^q(u,p)$ of non-absolute type have recently been introduced by Neyaz and Hamid (see, [13]).