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We show that the higher moments of the evolution obtained from the ModifiedLeading Logarithm Approximation may be regarded as spurious higher order termsin perturbation theory, and that neglecting them leads to a good description ofthe data around and above the peak in $\xi=\ln (1/x)$. Furthermore, we use thisstudy of the moments to show that at high energy the Limiting Spectrum withLocal Parton-Hadron Duality may also be derived from the Modified LeadingLogarithm Approximation without any non-perturbative assumptions.Comment: Submitted to Eur. Phys. J.,

Low x particle spectra in the modified leading logarithm approximation