This paper presents the model of Layered Memory Automata (LaMA) to deal with languages involving infinite alphabets, with practical applications in the analysis of datastreams, or modeling complex resource usages in concurrent systems. The LaMA can be seen as an extension of the Finite Memory Automata (FMA) with memory layers and the capacity of dealing with an unbounded amount of memory. Despite the increased expressiveness, the LaMA preserve most of the “good” properties of the FMA, in particular the closure properties for the so-called quasi-regular constructions. Moreover, the layering of the memory enables particularly economical constructions, which is an important focus of our study. The capacity of dealing with an unbounded amount of memory brings the LaMA closer to more powerful automata models such as the history register automata (HRA), thus occupying an interesting position at the crossroad between the operational and the more abstract points of view over data-languages.