Pretrained language models (PTLMs) are typically learned over a large, static corpus and further fine-tuned for various downstream tasks. However, when deployed in the real world, a PTLM-based model must deal with data from a new domain that deviates from what the PTLM was initially trained on, or newly emerged data that contains out-of-distribution information. In this paper, we study a lifelong language model pretraining challenge where a PTLM is continually updated so as to adapt to emerging data. Over a domain-incremental research paper stream and a chronologicallyordered tweet stream, we incrementally pretrain a PTLM with different continual learning algorithms, and keep track of the downstream task performance (after fine-tuning) to analyze its ability of acquiring new knowledge and preserving learned knowledge. Our experiments show continual learning algorithms improve knowledge preservation, with logit distillation being the most effective approach. We further show that continual pretraining improves generalization when training and testing data of downstream tasks are drawn from different time steps, but do not improve when they are from the same time steps. We believe our problem formulation, methods, and analysis will inspire future studies towards continual pretraining of language models.