In this paper we describe the detailed design of the application software (ASW) of the instrument control unit (ICU) of NISP, the Near-Infrared Spectro-Photometer of the Euclid mission. This software is based on a real-time operating system (RTEMS) and will interface with all the subunits of NISP, as well as the command and data management unit (CDMU) of the spacecraft for telecommand and housekeeping management. We briefly review the main requirements driving the design and the architecture of the software that is approaching the Critical Design Review level. The interaction with the data processing unit (DPU), which is the intelligent subunit controlling the detector system, is described in detail, as well as the concept for the implementation of the failure detection, isolation and recovery (FDIR) algorithms. The first version of the software is under development on a Breadboard model produced by AIRBUS/CRISA. We describe the results of the tests and the main performances and budgets.