Essential oils (EOs) are excellent antimicrobial agents sometimes used in active food packaging. This work studies the susceptibility of 48 clinical isolates and 12 reference strains of Gram-negative bacilli to oregano essential oil, cinnamon essential oil, and combinations of both. Furthermore, the tendency of the clinical isolates to develop resistance to these EOs and to different antibiotics after sequential oregano or cinnamon exposure was studied. For this purpose, antibiotic susceptibility (through disk diffusion assays and minimum inhibitory concentration [MIC] determination) and oregano and cinnamon susceptibility (through MIC and minimum bactericidal concentration [MBC] determination) were compared after 50 passages in the presence or absence of subinhibitory concentrations of oregano and cinnamon essential oils. The results showed that all strains were susceptible to both EOs and their combination independently of the antibiotic resistance profile. In addition, neither synergistic nor antagonistic effects were observed between oregano and cinnamon essential oils at the concentrations tested. After the sequential exposure to both EOs, only Serratia marcescens, Morganella morganii, and Proteus mirabilis treated with oregano changed their antibiotic resistance profile and/or increased their resistance to this EO. However, the changes in antibiotic and oregano resistance were not related.