Processes of structural reorganization of covalently- and metallic-bonded isolated two-dimensional monolayer nanosystems were discussed. The effects of adsorption-induced reconstruction of carbon nanotubular surface were also under consideration. It was shown that nature of interaction in quantum-sized nanosystems substantially predetermines stable forms of its structural organization. It was mentioned that the processes of chemical adhesion interaction between adsorbate and nanotubular surface essentially change the character of reconstruction.