In this talk we address the issue of stability for the first order perturbation of the biharmonic operator from partial data, in a bounded domain of dimension three or higher. Specifically, we shall consider two partial data settings: (1) Assuming that the inaccessible portion of the boundary is flat, and we have knowledge of the Dirichlet-to-Neumann map on the complement. (2) Assuming that the perturbations are known in a neighborhood of the boundary, measurements are performed only on arbitrarily small open subsets of the boundary. In both settings we obtain log type stability estimates. Part of this talk is based on a joint work with Salem Selim.