Requirements engineering refers to activities of gathering and organizing customer requirements and system specifications, making explicit representations of them, and making sure that they are valid and accounted for during the course of the design lifecycle of software. One very popular software development practice is the incremental development practice. The incremental development refers to practices that allow a program, or similarly specifications, to be developed, validated, and delivered in stages. The incremental practice is characterized by its depth-first process where focuses are given to small parts of the system in sequence to fair amounts of detail. In this paper, we present a development and validation of specifications in such an incremental style using a tool called ASADAL, a comprehensive CASE tool for real-time systems. ASADAL supports incremental and hierarchical refinements of specifications using multiple representational constructs and the evolving incomplete specifications can be formally tested with respect to critical real time properties or be simulated to determine whether the specifications capture the intended system behavior. In particular, we highlight features of ASADAL's specification simulator, called ASADAL/SIM, that plays a critical role in the incremental validation and helps users gain insights into the validity of evolving specifications. Such features include the multiple and mixed level simulation, real-value simulation, presentation and analysis of simulation data, and variety of flexible simulation control schemes. We illustrate the overall process using an example of an incremental specification development of an elevator control system.