Let X and Y be Banach spaces. A set ℳ of 1-summing operators from X into Y is said to be uniformly summing if the following holds: given a weakly 1-summing sequence ( x n ) in X , the series ∑ n ‖ T x n ‖ is uniformly convergent in T ∈ ℳ . We study some general properties and obtain a characterization of these sets when ℳ is a set of operators defined on spaces of continuous functions.