In this paper, we introduce an authorship attribution method called Authorial Language Models (ALMs) that involves identifying the most likely author of a questioned document based on the perplexity of the questioned document calculated for a set of causal language models fine-tuned on the writings of a set of candidate author. We benchmarked ALMs against state-of-art-systems using the CCAT50 dataset and the Blogs50 datasets. We find that ALMs achieves a macro-average accuracy score of 83.6% on Blogs50, outperforming all other methods, and 74.9% on CCAT50, matching the performance of the best method. To assess the performance of ALMs on shorter texts, we also conducted text ablation testing. We found that to reach a macro-average accuracy of 70%, ALMs needs 40 tokens on Blogs50 and 400 tokens on CCAT50, while to reach 60% ALMs requires 20 tokens on Blogs50 and 70 tokens on CCAT50.