The stochastic dynamics of individual co-doped Er: Yb upconversion nanoparticles (UCNP) were investigated from experiments and simulations. The UCNP were characterized by high-resolution scanning electron microscopy, dynamic light scattering, and zeta potential measurements. Single UCNP measurements were performed by fluorescence upconversion micro-spectroscopy and optical trapping. The mean-square displacement (MSD) from single UCNP exhibited a time-dependent diffusion coefficient which was compared with Brownian dynamics simulations of a viscoelastic model of harmonically bound spheres. Experimental time-dependent two-dimensional trajectories of individual UCNP revealed correlated two-dimensional nanoparticle motion. The measurements were compared with stochastic trajectories calculated in the presence of a non-conservative rotational force field. Overall, the complex interplay of UCNP adhesion, thermal fluctuations and optical forces led to a rich stochastic behavior of these nanoparticles Ver menos