The response of many materials (metals, alloys, composites, etc.) to external loading
may be essentially influenced by an existing or emerging internal structure at smaller
scales which must be taken into account. For this purpose the concept of dual
internal variables can be used in order to describe the effect of internal fields. In this
paper it is shown that dual internal variable theory is sufficiently general to model
cases like micromorphic elasticity and the influence of microtemperature. Based on
the material (canonical) balance equations for material momentum and energy, this
approach extends single internal variable theory. The resulting governing equations
are not limited by first-order reaction-diffusion equations, as is typical for
single internal variable theory. Hyperbolic governing equations for internal
variables provide the description of the interaction of waves at the macro and
microlevels.