NOVELTY - A polyisocyanate composition comprises a copolymerized polyisocyanate comprising an aliphatic diisocyanate unit and an alicyclic diisocyanate unit in molar ratio of 95/5-50/50, an alicyclic polyisocyanate comprising alicyclic diisocyanate unit and/or an aliphatic polyisocyanate comprising an aliphatic diisocyanate unit, and a polyisocyanate comprising 60 mol% or more isocyanurate group, and has viscosity at 25 degrees C of 100-10000 mPa.second.    USE - Polyisocyanate composition is used in coating composition for forming cured material (all claimed). Uses include but are not limited to motor vehicle, building materials, household appliance, woodwork, laminate for solar cells, television, personal computer, digital camera and mobile telephone.    ADVANTAGE - The polyisocyanate composition has excellent storage stability and low viscosity, and provides coating composition having excellent film hardness, surface smoothness, chemical resistance, adhesiveness and quick-drying capability. The coating composition provides excellent decoration property, weather resistance, acid resistance, rust prevention property, chipping resistance and adhesiveness to precoat metal coating material, automotive paint, plastic coating, and construction coating material for floor.    DETAILED DESCRIPTION - A polyisocyanate composition comprises a copolymerized polyisocyanate comprising an aliphatic diisocyanate unit and an alicyclic diisocyanate unit in molar ratio of 95/5-50/50, an alicyclic polyisocyanate comprising alicyclic diisocyanate unit and/or an aliphatic polyisocyanate comprising an aliphatic diisocyanate unit, and a polyisocyanate comprising 60 mol% or more isocyanurate group with respect to total of 100 mol% of isocyanurate group, allophanate group, biuret group, urethane group, urethodione group, imino oxadiazinedione group and urea group, and has viscosity at 25 degrees C of 100-10000 mPa.second. An INDEPENDENT CLAIM is included for coating composition containing an active hydrogen compound and the polyisocyanate composition.