Upon improving and extending the concept of redundancy of frames, we
introduce the notion of redundancy of fusion frames, which is concerned with the properties
of lower and upper redundancies. These properties are achieved by considering
the minimum and maximum values of the redundancy function which is defined from
the unit sphere of the Hilbert space into the positive real numbers. In addition, we study
the relationship between redundancy of frames (fusion frames) and dual frames (dual
fusion frames). Moreover, we indicate some results about excess of fusion frames.
We state the relationship between redundancy of local frames and fusion frames in a
particular case. Furthermore, some examples are also given.