Textual deepfakes can cause harm, especially on social media. At the moment, there are models trained to detect deepfake messages mainly for the English language, but no research or datasets currently exist for detecting them in most low-resource languages, such as Bulgarian. To address this gap, we explore three approaches. First, we machine translate an English-language social media dataset with bot messages into Bulgarian. However, the translation quality is unsatisfactory, leading us to create a new Bulgarian-language dataset with real social media messages and those generated by two language models (a new Bulgarian GPT-2 model — GPT-WEB-BG, and ChatGPT). We machine translate it into English and test existing English GPT-2 and ChatGPT detectors on it, achieving only 0.44-0.51 accuracy. Next, we train our own classifiers on the Bulgarian dataset, obtaining an accuracy of 0.97. Additionally, we apply the classifier with the highest results to a recently released Bulgarian social media dataset with manually fact-checked messages, which successfully identifies some of the messages as generated by Language Models (LM). Our results show that the use of machine translation is not suitable for textual deepfakes detection. We conclude that combining LM text detection with fact-checking is the most appropriate method for this task, and that identifying Bulgarian textual deepfakes is indeed possible.