In DNA computing, a sticker system is a computing mechanism involving the Watson-Crick complementarity of DNA molecules. The sticker system is known as a language generating device based on the sticker operation which is analyzed through the concept of formal language theory. The grammar of a formal language can be described by determining finite sets of variables, terminal symbols and production rules. Research on the grammar which uses the Watson-Crick complementarity has been done previously, known as Watson-Crick grammars. As an improvement to the Watson-Crick grammars, the static Watson-Crick grammars have been proposed as an analytical counterpart of sticker system which consist of regular grammar, linear grammar and context-free grammar. In this research, the closure properties of static Watson-Crick linear and context-free grammars are investigated. The result shows that the families of languages generated by static Watson-Crick linear and context-free grammars are closed under different operations.