In many domains systems need to run continuously and can- not be shut down for reconfiguration or maintenance tasks. Cyber-physical or cloud-based systems, for instance, thus of- ten provide means to support their adaptation at runtime. The required flexibility and adaptability of systems suggests the application of Software Product Line (SPL) principles to manage their variability and to support their reconfiguration. Specifically, Dynamic Software Product Lines (DSPL) have been proposed to support the management and binding of variability at runtime. While SPL evolution has been widely studied, it has so far not been investigated in detail in a DSPL context. Variability models that are used in a DSPL have to co-evolve and be kept consistent with the systems they represent to support reconfiguration even after changes to the systems at runtime. In this short paper we present a classification of the required operations for jointly evolving problem and solution space in a DSPL. We analyze the impact of such operations on the consistency of a DSPL and propose an approach to deal with the described issues. We describe a runtime monitoring system used in the domain of industrial automation software as an example of a DSPL evolving at runtime to motivate and explain our work.