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In this paper, a classification of semidiscrete equations of hyperbolic typeis carried out. We study the class of equations of the form$$\frac{du_{n+1}}{dx}=f\left(\frac{du_{n}}{dx},u_{n+1},u_{n}\right),$$ here isthe unknown function $u_n (x)$ depends on one discrete $n$ and one continuous$x$ variables. The classification is based on the requirement for the existenceof higher symmetries in the discrete and continuous directions. The case isconsidered when the symmetries are of order 3 in both directions. As a result,a list of equations with the required conditions is obtained.

Classification of semidiscrete hyperbolic type equations. The case of third order symmetries