This work addresses the problem of fault detection and diagnosis (FDD) for a quad-rotor mini air vehicle (MAV). Actuator faults are considered on this paper. The basic idea behind the proposed method is to estimate the faults signals using the extended state observers theory. To estimate the faults, a polynomial observer (Aguilar et al. 2011; Mata-Machuca et al., Commun Nonlinear Sci Numer Simul 15(12):4114-4130, 2010, BioSystems 100(1):65-69, 2010) is presented by using the available measurements and know inputs of the system. In order to investigate the diagnosability properties of the system, a differential algebra approach is proposed (Cruz-Victoria et al., J Frankl Inst 345(2):102-118, 2008; and Martinez-Guerra and Diop, IEE P-Contr Theor Ap 151(1):130-135, 2004). The effectiveness of the methodology is illustrated by means of numerical simulations.