This paper presents a novel deep-learning (DL)-based approach for classifying digitally modulated signals, which involves the use of capsule networks (CAPs) together with the cyclic cumulant (CC) features of the signals. These were blindly estimated using cyclostationary signal processing (CSP) and were then input into the CAP for training and classification. The classification performance and the generalization abilities of the proposed approach were tested using two distinct datasets that contained the same types of digitally modulated signals, but had distinct generation parameters. The results showed that the classification of digitally modulated signals using CAPs and CCs proposed in the paper outperformed alternative approaches for classifying digitally modulated signals that included conventional classifiers that employed CSP-based techniques, as well as alternative DL-based classifiers that used convolutional neural networks (CNNs) or residual networks (RESNETs) with the in-phase/quadrature (I/Q) data used for training and classification.