We study the cosmological evolution of string/M moduli fields T. We use T-duality to fix the potential and show that the superpotential W is a function of the duality invariant function j(T) only. If W is given as a finite polynomial of j then the moduli fields do not give an accelerating universe, i.e. they cannot be used as quintessence. Furthermore, at T much greater than 1 the potential is given by a double exponential potential V similar or equal to e(-aeroot2T) leading to a fast decaying behavior at large times. For moduli potentials with a finite v.e.v. of T the energy density redshift is model dependent but if T has a finite mass, m < infinity, then the moduli energy density redshifts faster or equal to matter. Only if the moduli mass is infinite can the moduli energy density dominate the universe independently of the initial conditions. [References: 53]
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