We present a theoretical description of on-and off-resonance, (4) over bar -quasi-phasematched, second-harmonic generation (SHG) in microdisks made of GaAs or other materials possessing (4) over bar symmetry, such as GaP or ZnSe. The theory describes the interplay between quasi-phasematching (QPM) and the cavity-resonance conditions. For optimal conversion, all waves should be resonant with the microdisk and should satisfy the (4) over bar -QPM condition. We explore chi((2)) nonlinear mixing if one of the waves is not resonant with the microdisk cavity and calculate the second-harmonic conversion spectrum. We also describe perfectly destructive (4) over bar -QPM where both the fundamental and second-harmonic are on-resonance with the cavity but SHG is suppressed.