The present invention relates to a heat- and moisture-crosslinkable adhesive composition comprising: a) from 40 to 60 wt % of at least one polyurethane obtainable by a polyaddition reaction of at least one particular diisocyanate with at least one polyether diol, with or without the presence of at least one reaction catalyst, at a reaction temperature T1 below 95° C., in anhydrous conditions, and in amounts of diisocyanate(s) and of polyether diol(s) leading to an NCO/OH molar ratio in the range from 1.6 to 1.9; b) from 39 to 59 wt % of at least one compatible tackifying resin and c) from 0.01 to 1 wt % of at least one crosslinking catalyst. The present invention also relates to a method of preparing said adhesive composition, a self-adhesive support coated with the crosslinked adhesive composition and the use of said support for making labels and/or self-adhesive tapes.