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 \sim 1.32 M _ { \bigodot } and \sim 1.33 M _ { \bigodot } , respectively .
Comparing the total masses of the eclipsing pair of 3.12 M _ { \bigodot } , 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 .