  An $n\times n$ matrix $C$ is said to be {\it centrosymmetric} if it satisfies
the relation $JCJ=C$, where $J$ is the $n\times n$ counteridentity matrix.
Centrosymmetric matrices have a rich eigenstructure that has been studied
extensively in the literature. Many results for centrosymmetric matrices have
been generalized to wider classes of matrices that arise in a wide variety of
disciplines. In this paper, we obtain interesting spectral properties for
nonnegative centrosymmetric matrices. We show how to change one single
eigenvalue, two or three eigenvalues of an $n\times n$ nonnegative
centrosymmetric matrix without changing any of the remaining eigenvalues
neither nonnegativity nor the centrosymmetric structure. Moreover, our results
allow partially answer some known questions given by Guo [11] and by Guo and
Guo [12]. Our proofs generate algorithmic procedures that allow to compute a
solution matrix.
