Recent years have witnessed the emergence of a new paradigm of building natural language processing (NLP) systems: general-purpose, pre-trained language models (LMs) are composed with simple downstream models and fine-tuned for a variety of NLP tasks. This paradigm shift significantly simplifies the system development cycles. However, as many LMs are provided by untrusted third parties, their lack of standardization or regulation entails profound security implications, which are largely unexplored. To bridge this gap, this work studies the security threats posed by malicious LMs to NLP systems. Specifically, we present TROJAN-LM, a new class of trojaning attacks in which maliciously crafted LMs trigger host NLP systems to malfunction in a highly predictable manner. By empirically studying three state-of-the-art LMs (BERT, GPT-2, XLNet) in a range of security-critical NLP tasks (toxic comment detection, question answering, text completion) as well as user studies on crowdsourcing platforms, we demonstrate that TROJAN-LM possesses the following properties: (i) flexibility - the adversary is able to flexibly dene logical combinations (e.g., 'and', 'or', 'xor') of arbitrary words as triggers, (ii) efficacy - the host systems misbehave as desired by the adversary with high probability when trigger-embedded inputs are present, (iii) specificity - the trojan LMs function indistinguishably from their benign counterparts on clean inputs, and (iv) fluency - the trigger-embedded inputs appear as fluent natural language and highly relevant to their surrounding contexts. We provide analytical justification for the practicality of TROJAN-LM, and further discuss potential countermeasures and their challenges, which lead to several promising research directions.