In this paper we investigate the solution of generalized distributed order diffusion equations with composite time fractional derivative by using the Fourier-Laplace transform method. We represent solutions in terms of infinite series in Fox H-functions. The fractional and second moments are derived by using Mittag-Leffler functions. We observe decelerating anomalous subdiffusion in case of two composite time fractional derivatives. Generalized uniformly distributed order diffusion equation, as a model for strong anomalous behavior, is analyzed by using Tauberian theorem. Some previously obtained results are special cases of those presented in this paper.MSC2010. Primary: 26A33, 33E12; Secondary: 34A08, 35R11.PACS numbers:The initial condition is usually taken as W (x, 0+) = δ(x), and the boundary conditions are given by W (±∞, t) = ∂ ∂x W (±∞, t) = 0 in unbounded domain in space of Lebesgue integrable functions. These are natural boundary conditions which are used in order to have an unique solution of the equation, as well as the solution to be bounded and differentiable. Note that these conditions are also used in order the Fourier transform (F [f (x)] =