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• Combination of CAN and LDR to detect kissing bonds in adhesive joints. • Nonlinear acoustics showing second harmonic and frequency downshifts of the LDR. • Harmonic Balance Method used to solve the nonlinear Duffing's equation for the LDR. • Nonlinear contact bilinear model developed for FE analysis of the adhesive joint. Adhesively bonded joints are susceptible to contamination of surfaces during manufacture and environmental deterioration in real operating conditions. These may cause the generation of so-called "kissing bonds" that can dramatically alter the strength of the joint leading to premature failure. Nonlinear acousto-ultrasonic (AU) techniques have shown great potential for monitoring kissing bonds with piezoelectric sensors permanently installed on the structural joint, thus enabling online and in-situ inspection. This paper investigated the combined contact acoustic nonlinearity (CAN) and local damage resonance (LDR) effects in the presence of kissing bonds in adhesive joints. Experimental nonlinear AU tests showed the formation of LDR frequency down-shifts and "jumps" of the fundamental damage resonance in adhesively bonded aluminium joints, with the kissing bond located internally to the overlapping region between the two adherends. These results were supported by a theoretical model based on the solution of the nonlinear Duffing's equation, under the assumption that the debonded region is a damped nonlinear harmonic oscillator subject to harmonic forcing. The Harmonic Balance Method was used to solve the nonlinear differential problem, showing the generation of frequency down-shifts via the dependence of the ratio between the excitation and LDR frequencies with the amplitude of the fundamental damage resonance. Additionally, two-dimensional finite element simulations using a reduced order model based on the Craig-Bampton technique were carried out to support experimental AU tests for the identification of the LDR frequency and the generation of nonlinear resonance effects. Good agreement between analytical, numerical, and experimental results revealed that a monitoring approach combining CAN and LDR is an extremely efficient and sensitive tool for ensuring integrity and safety of structural adhesive joints. [ABSTRACT FROM AUTHOR]