Abstract: By employing large language models (LLMs) we build a general genetic algorithm, i.e., a genetic algorithm (GA) that can solve various domains without any changes to its algorithmic components. Our approach requires only a problem description in natural language and a black-box fitness function and can then handle any type of data via natural-language-based evolutionary operators that call an LLM to compute their application. The relevant prompts for the operators can be human-designed or self-optimized with similar performance results. Compared to the only other generalist GA approach, i.e., asking an LLM to write a new specific GA, our natural-language-based genetic algorithm (NaLaGA) offers not only a better class of safety (since no LLM-generated code is executed by NaLaGA) but also greatly improved results in the two example domains ``Schwefel'' and ``grid world maze''.