The emergence of multidrug resistance among gram-negative bacilli is complex. Numerousfactors need to be considered, including the biological fitness cost of resistance, fitnesscompensatorymutations and frequency and type of antibiotic exposure. A mathematical modelevaluating these complex relationships was developed in an individual colonized with strains ofpan-susceptible, single-, two- and multidrug-resistant (MDR) gram-negative bacilli (GN). The effectof bacterial fitness, compensatory mutations and the frequency of three-antimicrobial regimenexposure to predominance of multidrug-resistant strains were quantified. The model predicts thatinitially, in the absence of antibiotic exposure, the biologically fitter pan-susceptible strain predominatesover the resistant strains. Over time, the fitness of the MDR strains increases fasterwith repeated antimicrobial exposure, through compensatory-fitness mutations. Increasing thefrequency of exposure to the three-antimicrobial regimen or, increasing the initial fitness of theresistant strains, substantially decreases the time to MDR-GN predominance. The model impliesthat when MDR-GN strains evolve into strains that are fitter than susceptible strains, a reductionin antimicrobial exposure may not result in a decrease of MDR-GN, since the absence of selectiveantimicrobial pressure would no longer favor susceptible strains. The model also implies thatantimicrobial cycling may promote the emergence of MDR-GN.