  In this article we study the differences of two consecutive eigenvalues
$\lambda_{i}-\lambda_{i-1}$ up to $i=2g-2$ for the Laplacian on hyperbolic
surfaces of genus $g$, and show that the supremum of such spectral gaps over
the moduli space has infimum limit at least $\frac{1}{4}$ as genus goes to
infinity. A min-max principle for eigenvalues on degenerating hyperbolic
surfaces is also established.
