The sequence space $a^r_c$ have been defined and the classes $(a^r_c:\ell_p)$ and $(a^r_c:c)$ infinite matrices have been characterized by Aydin and Ba\c sar (On the new sequence spaces which include the spaces $c_0$ and $c$, Hokkaido Math. J. 33(2) (2004), 383-398) [1], where $1\leq p\leq\infty$. The main purpose of the present paper is to characterize the classes $(a^r_c:f)$ and $(a^r_c:f_0)$, where $f$ and $f_0$ denote the spaces of almost convergent and almost convergent null sequences with real or complex terms.