This study proposes a convolutional neural network (CNN)-based steganalytic method that allows ternary classification to simultaneously identify WOW and UNIWARD, which are representative adaptive image steganographic algorithms. WOW and UNIWARD have very similar message embedding methods in terms of measuring and minimizing the degree of distortion of images caused by message embedding. This similarity between WOW and UNIWARD makes it difficult to distinguish between both algorithms even in a CNN-based classifier. Our experiments particularly show that WOW and UNIWARD cannot be distinguished by simply combining binary CNN-based classifiers learned to separately identify both algorithms. Therefore, to identify and classify WOW and UNIWARD, WOW and UNIWARD must be learned at the same time using a single CNN-based classifier designed for ternary classification. This study proposes a method for ternary classification that learns and classifies cover, WOW stego, and UNIWARD stego images using a single CNN-based classifier. A CNN structure and a preprocessing filter are also proposed to effectively classify/identify WOW and UNIWARD. Experiments using BOSSBase 1.01 database images confirmed that the proposed method could make a ternary classification with an accuracy of approximately 72%.