The formalism for linear absolute and convective instabilities developed in plasma physics (Briggs, 1964; Bers, 1973) is extended. The conclusion is that any order saddle point as well as any singular point of a frequency as a function of a wavenumber Ω(k) may contribute to instability. Moreover, contributions may come fromk-independent branches of the dispersion relation and from regular nonsaddle points of Ω(k). Accordingly, a variety of algebraic-exponential asymptotic behaviors, in particular, purely algebraic growths and sinusoidal oscillations, of a disturbance is possible. In shear flows and stratified flows instability may also be caused by the singularities associated with critical layers. It is shown that in such flows the asymptotic pattern of a growing disturbance may vary in the direction of the shear and/or stratification. Such variability of pattern may be present only in the presence of instabilities related to the interactions between critical layers and incident amplifying waves. Otherwise the pattern is the same to within a scalar factor.