Disclosed is an adhesive system and method of use thereof wherein the adhesive composition comprises a moisture curable adhesive comprised of an isocyanate terminated prepolymer and a cure accelerator having two curatives components having different cure kinetics. The cure accelerator is comprised of an isocyanate reactive compound comprising a primary, secondary or tertiary amino group, or a primary thiol group having faster curing kinetics resulting an increase in bead stability within the first minutes and a polyol selected from a diol and/or triol with slower curing kinetics allowing for sufficient open time and yet a fast strength build up. The preferred method of application of the adhesive system is via a 1K application gun.