Most experts consider that the causes of anomalous energy and particle transport in fusion devices are low frequency “drift” waves, themselves driven unstable by the equilibrium gradients and the associated drifts across the confining magnetic field (hence the terminology). We first introduce the dimensionless parameters which characterize drift waves (drift ordering). We then accordingly simplify the conventional two fluids description and obtain the general eigenvalue equations for drift eigenmodes. We finally search for solutions with angular frequency ω~ω* (the diamagnetic drift frequency), ω~λω*, etc … assuming λ≡LN(T)/qR ≪ 1 [LN(T) is the density (temperature) gradient length and qR is the connection length]. We recover in this way both the electron and the ion drift branches. The poloidal variation of the magnetic field has two opposite effects on the growth (damping) rate according to whether the width of the modes is larger or smaller than the distance between the rational surfaces q(r)=m/ℓ and q(r+Δ)=(m+l)/ℓ. Kinetic effects and the role of trapped particles are not described by the two fluid description but could be readily included.