Chaundy and Jolliffe proved their classical theorem on the uniform convergence of sine series with monotone coefficients in
1916. Lately, it has been generalized using classes MVBVS and SBVS2 instead of monotone sequences. In two variables, the class MVBVDS was studied under the uniform regular convergence of double
sine series. We shall generalize those results defining a new class of double sequences for the coefficients.