In this paper we present a theoretical and computational study of extreme multielectron ionization (involving the stripping of all the electrons from light, first-row atoms, and the production of heavily charged ions, e.g., Xe+q (qless than or equal to36) from heavy atoms) in elemental and molecular clusters of Xe-n,(D-2)(n), and (CD4)(n) (n=55-1061) in ultraintense (intensity I=10(15)-10(19) W cm(-2)) laser fields. Single atom or molecule multielectron ionization can be adequately described by the semiclassical barrier suppression ionization (BSI) mechanism. Extreme cluster multielectron ionization is distinct from that of a single atomic or molecular species in terms of the mechanisms, the ionization level and the time scales for electron dynamics and for nuclear motion. The novel compound mechanism of cluster multielectron ionization, which applies when the cluster size (radius R-0) considerably exceeds the barrier distance for the BSI of a single constituent, involves a sequential-parallel, inner-outer ionization. The cluster inner ionization driven by the BSI for the constituents is induced by a composite field consisting of the laser field and inner fields. The energetics and dynamics of the system consisting of high energy (less than or equal to3 keV) electrons and of less than or similar to100 keV ions in the laser field was treated by molecular dynamics simulations, which incorporate electron-electron, electron-ion, ion-ion, and charge-laser interactions. High-energy electron dynamics also incorporates relativistic effects and includes magnetic field effects. We treat inner ionization considering inner field ignition, screening and fluctuation contributions as well as small [(less than or equal to13%)] impact ionization contributions. Subsequent to inner ionization a charged nanoplasma is contained within the cluster, whose response to the composite (laser+inner) field results in outer ionization, which can be approximately described by an entire cluster barrier suppression ionization mechanism. (C) 2004 American Institute of Physics.