The design assumptions and principles of two hybrid, rule-and model-based expert system shells for uncertain backward and forward reasoning are presented. The systems may be used to reason with any knowledge base, which consist of an uncertain rule base, partially uncertain model base, exact constraint base, uncertain constraint base and advice base together with advice files. Its semantics is simple and straightforward. Practically unlimited nesting of rules and models is allowed. The systems are equipped with diagnostic facilities automatically checking the rule- and constraint bases for inconsistencies and redundancies and providing warnings and detailed diagnostic messages.