Summary: We present three approximation theorems for the Gauss-Weierstrass singular integral in the spaces \(L^p\) \((1\leq p<\infty)\), \(C\), and the Hölder spaces. Those theorems generalize and improve the results for the Gauss-Weierstrass singular integral given in E. Deeba, R. N. Mohapatra and R. S. Rodriguez [Rend. Mat. Appl., VII. Ser. 8, No. 3, 345-355 (1988; Zbl 0677.42015)], Z. Ditzian and V. Totik [“Moduli of smoothness” (1987; Zbl 0666.41001)], and R. N. Mohapatra and R. S. Rodriguez [Math. Nachr. 149, 117-124 (1990; Zbl 0726.42003)].