In the paper a method of finding periodical solutions of the differential equation
of the form x(t)  p(t)x(t 1) = q(t)x([t])  f (t) is given, where [] denotes the greatest
integer function, p(t) , q(t) and f (t) are continuous periodic functions of t . This provides n -
periodic soluble problem to a system of n 1 linear equations, where n = 2. Furthermore, by
using the well known properties of linear system in the algebra, all existence conditions for 2 -
periodical solutions are described, and the explicit formula for these solutions are obtained.