A formal device is said to be adaptive whenever its behavior changes dynamically, in a direct response to its input stimuli, without interference of external agents, even its users. In order to achieve this feature, adaptive devices have to be self-modifiable. In other words, any possible changes in the device’s behavior must be known at their full extent at any step of its operation in which the changes have to take place. Therefore, adaptive devices must be able to detect all situations causing possible modifications and to adequately react by imposing corresponding changes to the device’s behavior. In this work, devices are considered whose behavior is based on the operation of subjacent non-adaptive devices that be fully described by some finite set of rules. An adaptive rule-driven device may be obtained by attaching adaptive actions to the rules of the subjacent formulation, so that whenever a rule is applied, the associated adaptive action is activated, causing the set of rules of the subjacent non-adaptive device to be correspondingly changed. In this paper a new general formulation is proposed that unifies the representation and manipulation of adaptive rule-driven devices and states a common framework for representing and manipulating them. The main feature of this formulation is that it fully preserves the nature of the underlying non-adaptive formalism, so that the adaptive resulting device be easily understood by people familiar to the subjacent device. For illustration purposes, a two-fold case-study is presented, describing adaptive decision tables as adaptive rule-driven devices, and using them for emulating the behavior of a very simple adaptive automaton, which is in turn another adaptive rule-driven device.