In recent years, machine translation has made significant advancements; however, its effectiveness can vary widely depending on the language pair. Languages with limited resources, such as Kazakh, Uzbek, Kalmyk, Tatar, and others, often encounter challenges in achieving high-quality machine translations. Kazakh is an agglutinative language with complex morphology, making it a low-resource language. This article addresses the task of post-editing machine translation for the Kazakh language. The research begins by discussing the history and evolution of machine translation and how it has developed to meet the unique needs of languages with limited resources. The research resulted in the development of a machine translation post-editing system. The system utilizes modern machine learning methods, starting with neural machine translation using the BRNN model in the initial post-editing stage. Subsequently, the transformer model is applied to further edit the text. Complex structural and grammatical forms are processed, and abbreviations are replaced. Practical experiments were conducted on various texts: news publications, legislative documents, IT sphere, etc. This article serves as a valuable resource for researchers and practitioners in the field of machine translation, shedding light on effective post-editing strategies to enhance translation quality, particularly in scenarios involving languages with limited resources such as Kazakh and Uzbek. The obtained results were tested and evaluated using specialized metrics—BLEU, TER, and WER.