This three-part paper analyzes existing approaches and methods of organizing failure- and fault-tolerant computing in distributed multicomputer systems (DMCS), identifies and provides rationale for a list of issues to be solved. We review the application areas of failure- and fault- tolerant control systems for complex network and distributed objects. The second part further investigates the issues of organizing failure- and fault- tolerance in the DMCS. The systemic, functional, and test diagnostics are viewed as the basis for building unattended failure- and fault-tolerant systems. We introduce the concept of self-managed degradation (when the DMCS eventually proceeds to a safe shutdown at a critical level of degradation) as a means to increase the DMCS active life.