  The non-perturbative behaviour of macroscopic loop amplitudes in the exactly
solvable string theories based on the KdV hierarchies is considered. Loop
equations are presented for the real non-perturbative solutions living on the
spectral half-line, allowed by the most general string equation
$[\tilde{P},Q]=Q$, where $\tilde{P}$ generates scale transformations. In
general the end of the half-line (the `wall') is a non-perturbative parameter
whose r\^ole is that of boundary cosmological constant. The properties are
compared with the perturbative behaviour and solutions of $[P,Q]=1$. Detailed
arguments are given for the $(2,2m-1)$ models while generalisation to the other
$(p,q)$ minimal models and $c=1$ is briefly addressed.
