The aim of the paper is to sketch some solutions that arose along the work on Logic of Strict Processes (LSP). Three main topics are discussed: (a) negation based on implication constructed in intuitionistic fashion; (b) satisfiability in multimodal contexts and (c) a proposal of a first order semantics for Dynamic Logic of Strict Processes (DLSP). The system of DLSP differs from the original LSP in using the set of contexts, which are treated as ordered sets of formulas. The interpretation of a context is a transition system, which is constructed solely of simple processes. After the set of non-allowed processes is constructed, the negation of molecular formula can be understood as a set o processes that, when combined with processes associated with a non-negated formula, produce non-allowed processes. Satisfiablity in a transition system is defined by a special modal operator [φ]φ which is true only when the relation of metaimplication between φ and φ holds. In conclusion the author briefly reviews first order system based on DLSP and points to several open problems waiting for further investigation.