The emergence of multidrug resistance among gram-negative bacilli is complex. Numerous factors need to be considered, including the biological fitness cost of resistance, fitnesscompensatory mutations and frequency and type of antibiotic exposure. A mathematical model evaluating these complex relationships was developed in an individual colonized with strains of pan-susceptible, single-, two- and multidrug-resistant (MDR) gram-negative bacilli (GN). The effect of bacterial fitness, compensatory mutations and the frequency of three-antimicrobial regimen exposure to predominance of multidrug-resistant strains were quantified. The model predicts that initially, in the absence of antibiotic exposure, the biologically fitter pan-susceptible strain predominates over the resistant strains. Over time, the fitness of the MDR strains increases faster with repeated antimicrobial exposure, through compensatory-fitness mutations. Increasing the frequency of exposure to the three-antimicrobial regimen or, increasing the initial fitness of the resistant strains, substantially decreases the time to MDR-GN predominance. The model implies that when MDR-GN strains evolve into strains that are fitter than susceptible strains, a reduction in antimicrobial exposure may not result in a decrease of MDR-GN, since the absence of selective antimicrobial pressure would no longer favor susceptible strains. The model also implies that antimicrobial cycling may promote the emergence of MDR-GN.