Abstract:It is shown that complex-valued boundary value problems for several classes of recurrent relations with two independent variables, of some considerable interest, are solvable on the following domain: C = {(n, k) : 0 ≤ k ≤ n, k ∈ N 0 , n ∈ N}, the so called combinatorial domain. The recurrent relations include some of the most important combinatorial ones, which, among other things, serve as a motivation for the investigation. The methods for solving the boundary value problems are presented and explained in detail.Keywords: recurrent relations with two independent variables; boundary value problem; combinatorial domain; equation solvable in closed form; method of half-lines MSC: 39A14; 05A10