Significance of the constitutional size in the composites having the constitution of nanometer size (Nano-Composites) was emphasized. Every Nano-Composite should have two critical values, the upper limit and the lower limit, for the dimension of the constitution to posses the distinguishable property as Nano-Composite. The critical values depend on the property expected for the composite. The values were estimated or re-viewed on various basis which are thought to be useful for each property, such as cata-lytic activity, magnetism, optical property as well as mechanical one. For examples: The range of the binding force acting across the surface of solids was estimated from the surface free energy and the ideal strength, which gives the critical value in general expression for the constitutional dimension and also for one basic aspect of catalitic activity. The values are about 7 nm(Si₃N₄), 4 nm(SiC), 4 nm (Al), 2 nm(Fe), 2 nm(W) and 3 nm(Pt). The value is very small for oxides, 0.5 nm(Al₂O₃) and 0.4 nm(MgO) probably due to screening effect on the surface. As to magnetic properties, 100 mn for super paramagnetism's occurrence and 20 nm for making the originally hard magnetic material soft one. Optically, the value is about 50 nm for reflective intex change. Mechanically, it is about 100 nm for strengthning or restricting dislocation movement. Some improved properties, which could be expected or have been realized, are described in the relation with the critical values.