We perform dynamical simulations of dry oxidation and NO annealing of the SiO2/4H-SiC C-face interface at 1500K using first-principles molecular dynamics based on plane waves, supercells, and the projector-augmented wave method. The slab model is used for the simulation. In the dry oxidation simulation, O atoms oxidize not only the C atoms at the SiC interface but also second-atomic-layer Si atoms in the SiC layer. Bilayer oxidation occurs in the oxidation process. The formation of C clusters that grow in the c-axis direction is observed. In the simulation of NO annealing, N atoms passivate interface C atoms. The density of N atoms saturates, then N atoms desorb as N2 molecules. CN molecules are formed by the abstraction of C atoms by the N atoms, and the CN molecules readily react at the interface. The formation of a Si3N structure is also observed.