  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.
