For two-dimensional continued fractions with partial quotients equal  $ {(1-g_{i-1, j})g_{ij}z_{ig}}\over {1}$ , ${(1-g_{i, j-1})g_{ij}z_{ig}}\over {1}$ , ${g_{ii} g_{i-1, i-1}z_{ii}}\over {1}$ convergence criteria have been established using the method of majorants.

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