Alzheimer's disease is a common type of dementia that can cause serious problems in cognitive functions and activities of daily living. Although there is no definitive cure for Alzheimer's disease today, early diagnosis is important to slow down the adverse conditions that may arise and to improve the quality of life. As a result of the development of artificial intelligence technologies and their consistent application in different fields, machine learning techniques have the potential to play an important role in the detection of Alzheimer's disease. In particular, deep learning-based methods, which have the ability to automatically extract patterns from complex patterns, are promising in this field. Recent studies show that the use of deep learning models for Alzheimer's detection on images is becoming widespread. In addition to contributing to the early diagnosis of the disease, these models also show potential in detecting different stages of the disease by analyzing the symptoms in magnetic resonance images. These developments enable the development of more effective treatment methods for patients. However, more studies are needed to evaluate the efficacy and safety of these technologies in clinical applications. In this study, classification studies were performed using MobileNetV2, InceptionV3, Xception, Vgg16 and Vgg19 models for the diagnosis of the disease on a publicly shared Alzheimer's dataset consisting of 6400 different samples and 4 different classes. An accuracy of 99.92% was calculated for the MobileNetV2 model. The performances of the models used in this study were compared with similar studies in the literature and their performances were reported in terms of different metrics. Among the five different models used, the highest accuracy value of 99.92% was obtained with MobileNetV2. It was concluded that the architectures used in the experimental studies produced generally better results than similar studies in the literature.