Diabetic retinopathy (DR) is a complication of diabetes that damages the delicate blood vessels of the retina and leads to blindness. Ophthalmologists rely on diagnosing the retina by imaging the fundus. The process takes a long time and needs skilled doctors to diagnose and determine the stage of DR. Therefore, automatic techniques using artificial intelligence play an important role in analyzing fundus images for the detection of the stages of DR development. However, diagnosis using artificial intelligence techniques is a difficult task and passes through many stages, and the extraction of representative features is important in reaching satisfactory results. Convolutional Neural Network (CNN) models play an important and distinct role in extracting features with high accuracy. In this study, fundus images were used for the detection of the developmental stages of DR by two proposed methods, each with two systems. The first proposed method uses GoogLeNet with SVM and ResNet-18 with SVM. The second method uses Feed-Forward Neural Networks (FFNN) based on the hybrid features extracted by first using GoogLeNet, Fuzzy color histogram (FCH), Gray Level Co-occurrence Matrix (GLCM), and Local Binary Pattern (LBP); followed by ResNet-18, FCH, GLCM and LBP. All the proposed methods obtained superior results. The FFNN network with hybrid features of ResNet-18, FCH, GLCM, and LBP obtained 99.7% accuracy, 99.6% precision, 99.6% sensitivity, 100% specificity, and 99.86% AUC.