In this study, we investigated the viscoelastic properties of metal nanoparticle monolayers at the air/water interface by dilational rheology under periodic oscillation of surface area. Au nanoparticles capped with oleylamine form a stable, dense monolayer on a Langmuir film balance. The stress response function of a nanoparticle monolayer was first analyzed using the classical Kelvin-Voigt model, yielding the spring constant and viscosity. The obtained results suggest that the monolayer of nanoparticles is predominantly elastic, forming a two-dimensional physical gel. As the global shape of the signal exhibited a clear nonlinearity, we further analyzed the data with the higher modes in the Fourier series expansion. The imaginary part of the higher mode signal was stronger than the real part, suggesting that the dissipative term mainly causes the nonlinearity. Intriguingly, the response function measured at larger strain amplitude became asymmetric, accompanied by the emergence of even modes. The significance of interactions between nanoparticles was quantitatively assessed by calculating the potential of mean force, indicating that the lateral correlation could reach up to the distance much larger than the particle diameter. The influence of surface chemical functions and core metal has also been examined by using Au nanoparticles capped with partially fluorinated alkanethiolate and Ag nanoparticles capped with myristic acid. The combination of dilational rheology and correlation analyses can help us precisely control two-dimensional colloidal assembly of metal nanoparticles with fine-adjustable localized surface plasmon resonance.