The relationship between parallel isometric array languages and sequential isometric array languages is examined. Their hierarchical structures are investigated and a hierarchy is established by introducing parallel context-free array languages (PCFAL), derivation bounded array languages (DBAL), linear array languages (LAL), and extended regular afray languages (ERAL). It is interesting to find that some fundamental aspects that hold in one-dimensional string languages do not hold in their two-dimensional counterparts. Some parsing techniques are also explored. It is shown that while parallel parsing grammars may be simpler to write and parallel processing usually takes less time than sequential ones, the nature of parallel parsing is very complicated. Finally, several future research topics concerned with parallel isometric array languages including their complexities, hierarchical structures, and application to pattern recognition are discussed.