While the hoarding of physical objects has been extensively explored, there is little research relating to the hoarding of digital materials. The research that has been conducted suggests that digital hoarding (DH) behaviours appears to have some similarities with physical hoarding (PH) behaviours, and can be just at psychologically distressing. This study uses the framework of the cognitive behavioural model of physical hoarding to explore digital hoarding behaviours, including possible similarities regarding emotional attachment to digital possessions, and possible links with Obsessive Compulsive Disorder (OCD) and indecisiveness. Two hundred and eighty two participants completed an online survey which measured levels of digital and physical hoarding, compulsive acquisition, OCD, indecisiveness, and mood. Strong emotional attachments to particular types of digital possessions were evident: this was especially true for photographs and videos. Significant positive relationships were found between all the variables measured. However, a regression analysis revealed that only OCD and physical hoarding scores were significant predictors of digital hoarding. Digital hoarding thus appears to share some of the features of physical hoarding. Implications, limitations and future research possibilities are discussed.