Pseudo 1st order Kinetic reaction

The pseudo 1st order reaction happens when one of the reactant is in large excess and its concentration doesnt change during the reaction . 


Is there any other such situation when a *certain* higher order reaction turns out to become a pseudo first order kinetic reaction (except the situation where an N$^{th}$ order reaction has N-1 species in large excess) ?




Example from biochemistry
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The Michaelis-Menten equation for enzyme kinetics is an example.


$v=\frac{k\_{cat}E\_0S}{K\_S+S}$ where $S$ is substrate concentration and $E$ in enzyme concentration.


At low $S$ ($S\ll K\_S$), the reaction is 2nd order with $v=\frac{k\_{cat}}{K\_S}E\_0S$, i.e. first order in both enzyme and in substrate. However at high $S$ ($S\gg K\_S$), the reaction is first order only in enzyme with $v=k\_{cat}E\_0$, and is zero-order in substrate. The substrate concentration doesn't have to be in molar excess to other reactants.


Example from process control
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In chemical engineering, nonlinear systems such as higher-order reactions occuring in a continuous process at steady-state are often modeled using linear (which you can think of as first-order reactions) systems as an approximation for developing process control techniques. A [MATLAB documentation page](http://www.mathworks.com/help/slcontrol/ug/linearizing-nonlinear-models.html) has some good information.


Another example, somewhat contrived
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As a last example, consider an unstable molecule $A$. It can decompose to $B$ by two entirely separate elementary mechanisms. The first is $\ce{A + A -> B + B}$. The second is $\ce{A -> B}$. At *high* concentrations of $A$, the second-order kinetics will dominate and the decomposition of $A$ will be second order. But *lower* the concentration enough, and the reaction will become first order in $A$ because the rate the bimolecular reaction will be dwarfed by the unimolecular route at low $A$.


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