The influence of task complexity on second language (L2) writing performance has been researched near-exclusively in relation to the linguistic complexity of the learners' written products, while only limited attention has been paid to the online writing processes. In order to fill this gap, the present study focused on the effects of task demands on writing processes as reflected in keystrokes. Forty-four L1 Korean speakers were randomly assigned to either simple or complex condition, and asked to write an argumentative essay. For the simple condition, content support was provided, whereas no such additional information was provided for the complex condition. During the writing task, participants' entire keystroke loggings were recorded, and analyzed in terms of fluency, pausing, and revision behaviors. The lexical and syntactic complexity of the written products was also analyzed and compared between the two task conditions. The results indicated that greater task demands significantly increased the number of pauses and revisions, having negative influence on fluency. Also, lexical rarity and phrasal complexity decreased under the complex condition. The results are discussed with respect to fuller understanding of the task-based approach to L2 writing.