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This article is concerned with the challenges associated with supporting communication in disconnected MANETs with such a sparse population of nodes and so little (or no) fixed infrastructure that the network graph is rarely, if ever, connected. The networks considered are autonomous and do not depend on established infrastructure. The disconnected nature and the lack of end-to-end connectivity between nodes mean that the communication must be delay-tolerant. We refer to such a networks as Disconnected Delay-Tolerant MANETs (DDTMs). In general the challenges associated with mobile computing are not new. However, issues in wireless communication such as low bandwidth, disconnections and high bandwidth variability are problematic and further exacerbated in DDTMs by little or no infrastructure, variable node population and lossy links. DDTMs additionally face challenges of mobility which is frequent and uncontrolled resulting in a highly dynamic topology and disconnected network graph. In addition, portability remains a challenge, where battery power, memory and processing power are limited. The challenges are presented using a two-tier classification scheme that allows their causes and inter-dependencies to be mapped.