Knowing individuals' relational orientation is imperative for effective offline, as well as online, interactions and collaborations. We use attachment theory to examine the link between Facebook users' relational orientation (in terms of attachment styles: Anxiety and avoidance) and their relational activities. Our research examines whether and how the two key relational processes identified in offline social relationships (self-expression and responsiveness) are manifested on online social networks and related to attachment styles. We describe our dataset of 640 Facebook users, their attachment scale survey results, and their 525,334 posts. We define four features that map onto relational activities on Facebook: status updates and status updates with emotional words (self-expression); comments and likes (responsiveness). We find significant relationships between the users' attachment styles and their self-expression and responsiveness activities on Facebook. A key takeaway of our research is that without relying on self-reported surveys, a computational analysis of a Facebook user's selfexpressing and responding activities alone can reveal the user's underlying relational orientation (i.e., attachment style).