Summary: The sufficient conditions of convergence of two-dimensional continued fractions (TDCF) with real elements are considered. The equivalence of ordinary and figured convergence of TDCF under these conditions is established. The theorem proved is a generalization of the theorem of D. I. Bodnar and Kh. I. Kuchminskaya [Mat. Metody Fiz.-Mekh. Polya 11, 3–6 (1980; Zbl 0439.40001)].