This chapter deals with the inverse problems of determining the coefficient at the lower term of a fractional diffusion equation with nonlocal boundary and nonlocal overdetermination (integral type) conditions. In Sect. 2.1, an inverse problem of determining the coefficient at the lower term of a multidimensional fractional diffusion equation in the case the direct problem is the initial-boundary problem for this equation with nonlocal initial and homogeneous Dirichlet conditions is considered. To determine the unknown coefficient, an overdetermination condition of the integral form is specified for the solution of the direct problem.