We report on the linear stability of micro-combustion in pipe, whese two instabilities manifest at high and low flow-rates. The combustion of a stoichiometric methane/air premixed mixture has been numerically investigated within a 3D reduced model. This model reproduces decently the flame dynamics in the range of speed between 5-100 cm/s. The flame position, the stability thresholds of the Flame with Repetitive Extinction and Ignition (FREI) and the flame shape are in accordance with the experiments. Furthermore, an analysis of the integral values of all mechanisms involved in the flame evolution has been carried out near the two stability thresholds. The phase shift between the reaction term and the radial diffusion has been identified as the source of instability in both cases. The global behavior has been then investigated with a linear stability analysis. The 2D and 3D temperature and concentration perturbations have been found by solving the eigenvalue problem obtained by linearizing the model around the basic state. Only one unstable axisymmetric mode has been found. This is in agreement with the direct numerical simulation of the model. (C) 2016 The Combustion Institute. Published by Elsevier Inc. All rights reserved.