Let f(x,y) be continuous and \(2\pi\)-periodic in each variable. In this paper the rate of uniform approximation, by Nörlund means, of the rectangular partial sums of double Fourier series of f(x,y) is studied. The first two theorems relate to the double Fourier series. As a special case the authors obtain the rate of uniform approximation to functions f(x,y) in Lip (\(\alpha\),\(\beta)\) the Lipschitz class and in Z(\(\alpha\),\(\beta)\) the Zymund class of orders \(\alpha\) and \(\beta \circ \alpha,\beta <1\) as well as the rate of uniform approximation to the conjugate functions.