The relay fusion frame proposed by Hong and Li is an extension of a fusion frame that has many applications in science. In this study, we introduce relay fusion frames in Hilbert
C
∗
-modules very naturally and shift some common attributes of fusion frames and relay fusion frames in Hilbert spaces to relay fusion frames in Hilbert
C
∗
-modules. In addition, we generalize some perturbation results in frame theory to relay fusion frames in Hilbert
C
∗
-modules. Finally, we introduce a class of
F
,
G
-relay fusion frames as a generalization of
K
-frames and present some perturbation results for
F
,
G
-relay fusion frames in Hilbert
C
∗
-modules.