Asymptotic methods are used to describe the nonlinear self-interaction
between a pair of oblique instability modes that eventually develops
when initially linear, spatially growing instability waves evolve down
stream in nominally two-dimensional, unbounded or semibounded, laminar
shear flows. The first nonlinear reaction takes place locally within
a so-called ''critical layer'' with the flow outside this layer consis
ting of a locally parallel mean flow plus a pair of oblique instabilit
y waves together with an associated plane wave. The instability wave a
mplitudes, which are completely determined by nonlinear effects within
the critical layer, satisfy a pair of integral differential equations
with quadratic to quartic-type nonlinearities. The most important fea
ture of these equations is the oblique mode, self-interaction term tha
t usually leads to a singularity at a finite downstream position. It i
s shown that this type of interaction is quite ubiquitous and is the d
ominant nonlinear interaction in many apparently unrelated shear flows
-even when the oblique modes do not exhibit the most rapid growth in t
he initial linear stage.