In historical linguistics, the affiliation of languages to a common language family is traditionally carried out using a complex workflow that relies on manually comparing individual languages. Large-scale standardized collections of multilingual wordlists and grammatical language structures might help to improve this and open new avenues for developing automated language affiliation workflows. Here, we present neural network models that use lexical and grammatical data from a worldwide sample of more than 1,000 languages with known affiliations to classify individual languages into families. In line with the traditional assumption of most linguists, our results show that models trained on lexical data alone outperform models solely based on grammatical data, whereas combining both types of data yields even better performance. In additional experiments, we show how our models can identify long-ranging relations between entire subgroups, how they can be employed to investigate potential relatives of linguistic isolates, and how they can help us to obtain first hints on the affiliation of so far unaffiliated languages. We conclude that models for automated language affiliation trained on lexical and grammatical data provide comparative linguists with a valuable tool for evaluating hypotheses about deep and unknown language relations.