This paper investigates deep neural networks for radio signal classification. Instead of performing modulation recognition and combining it with further analysis methods, the classifier operates directly on the IQ data of the signals and outputs the transmission mode. A data set of radio signals of 18 different modes, that commonly occur in the HF radio band, is presented and used as a showcase example. The data set considers HF channel properties and is used to train four different deep neural network architectures. The results of the best networks show an excellent accuracy of up to 98%.