ParaSol is a novel multithreaded system for shared-and distributed-memory parallel simulation, designed to support a variety of domain-specific simulation object libraries. We report on the design of the ParaSol kernel, which drives executions based on optimistic and adaptive synchronization protocols. The active-transaction flow methodology we advocate is enabled by an underlying, efficient lightweight process system. Though this process- and object-interaction view is known to both simplify and speed transition from model design to simulation implementation, migratable threads and objects pose many serious challenges to efficient kernel operation. Good solutions to these challenging problems are key to good simulator performance. We present techniques for the support of optimistic parallel simulations, addressing synchronization, state-saving, rollback, inter-process communication, and process scheduling.