Oil and coconut palm trees are important crops in many tropical countries, which are either planted as plantations or scattered in the landscape. Monitoring in terms of counting provides useful information for various stakeholders. Most of the existing monitoring methods are based on spectral profiles or simple neural networks and either fall short in terms of accuracy or speed. We use a neural network of the U-Net type in order to detect oil and coconut palms on very high resolution satellite images. The method is applied to two different study areas: (1) large monoculture oil palm plantations in Jambi, Indonesia, and (2) coconut palms in the Bengaluru Metropolitan Region in India. The results show that the proposed method reaches a performance comparable to state of the art approaches, while being about one order of magnitude faster. We reach a maximum throughput of 235 ha/s with a spatial image resolution of 40 cm. The proposed method proves to be reliable even under difficult conditions, such as shadows or urban areas, and can easily be transferred from one region to another. The method detected palms with accuracies between 89% and 92%.