  We derive non-linear recursion equations for the leading infrared logarithms
in massless non-renormalizable effective field theories. The derivation is
based solely on the requirements of the unitarity, analyticity and crossing
symmetry of the amplitudes. That emphasizes the general nature of the
corresponding equations. The derived equations allow one to compute leading
infrared logarithms to essentially unlimited loop order without performing a
loop calculation. For the implementation of the recursion equation one needs to
calculate tree diagrams only. The application of the equation is demonstrated
on several examples of effective field theories in four and higher space-time
dimensions.
