  The stability of two different bounce scenarios from F(R,G) modified gravity
at later times is studied, namely a hyperbolic cosine bounce model and a
matter-dominated one. After describing the main characteristics of F(R,G)
modified gravity, the two different bounce scenarios stemming from this theory
are reconstructed and their stability at late stages is discussed. The
stability of the hyperbolic cosine model is proven, while the concrete
matter-bounce model here chosen does not seem to accomplish the necessary
conditions to be stable at later times.
