Six mid-eclipse times of the eclipsing binary XZ And are obtained, which are analyzed together with others collected from the literature. Two sets of cyclic variations with periods of 33.43 and 100.4yr are found if a double-Keplerian model is used to fit the data. The 1:3 ratio of the periods suggests that both cyclic variations arise from dynamic motions of two companions rather than magnetic activity of the eclipsing pair. According to the double-Keplerian model, the companions have masses of similar to 1.32 M-circle dot and similar to 1.33 M-circle dot, respectively. Comparing with the total mass of the eclipsing pair of 3.12 M-circle dot, it is obvious that XZ And is a general N-body system. The strong gravitational perturbation between the two companions invalidates the double-Keplerian model. It is strange that two Keplerian periods with a 1:3 ratio are derived from the best fits with an "inappropriate" model. This illogical, but interesting phenomenon also appears in two other Algol systems, suggesting that our discoveries deserve attention from astronomers.