Linear and non-linear limb-darkening coefficients for the photometric bands u v b y U B V R I J H K are computed for very low effective temperatures stars. The atmosphere models used (PHOENIX-NextGen) do not include the effects of dust formation and dust opacities. These calculations are presented for the first time . The calculations extend the range of effective temperatures (2000K-50000K) covered by our previous papers. These data are important in order to deal with stars in the lower part of Main-Sequence like M or brown dwarfs. The non-linear behavior of the limb-darkening laws, particularly in this effective temperature range, is emphasized and we urge users to take it into account.