Large language models (LLMs), pre-trained or fine-tuned on large code corpora, have shown effectiveness in generating code completions. However, in LLM-based code completion, LLMs may struggle to use correct and up-to-date Application Programming Interfaces (APIs) due to the rapid and continuous evolution of libraries. While existing studies have highlighted issues with predicting incorrect APIs, the specific problem of deprecated API usage in LLM-based code completion has not been thoroughly investigated. To address this gap, we conducted the first evaluation study on deprecated API usage in LLM-based code completion. This study involved seven advanced LLMs, 145 API mappings from eight popular Python libraries, and 28,125 completion prompts. The study results reveal the \textit{status quo} and \textit{root causes} of deprecated API usage in LLM-based code completion from the perspectives of \textit{model}, \textit{prompt}, and \textit{library}. Based on these findings, we propose two lightweight fixing approaches, \textsc{ReplaceAPI} and \textsc{InsertPrompt}, which can serve as baseline approaches for future research on mitigating deprecated API usage in LLM-based completion. Additionally, we provide implications for future research on integrating library evolution with LLM-driven software development.
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