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Six mid-eclipse times of the eclipsing binary XZ And are obtained, which are analysed together with others collected from the literature. Two sets of cyclic variations with periods of 33.43 and 100.4 yr 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 the masses of about 1.32 Msun and 1.33 Msun, respectively. Comparing the total masses of the eclipsing pair of 3.12 Msun, it is obvious that XZ And is a general N-body system. The strong gravitational perturbation between 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 the inappropriate model. The illogical, but interesting phenomena also appear in other two Algol systems, suggesting that our discoveries deserve attention from astronomers.

A strange phenomenon in XZ Andromedae: two Keplerian periods with a 1:3 ratio