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Let   $S$   be a noncompact, finite area hyperbolic surface of type   $(g, n)$  . Let   $\Delta _S$   denote the Laplace operator on   $S$  . As   $S$   varies over the  moduli space   ${\mathcal {M}_{g, n}}$   of finite area hyperbolic surfaces of type   $(g, n)$  , we study, adapting methods of Ji [ 8 ] and Wolpert [ 15 ], the behavior of  small cuspidal eigenpairs  of   $\Delta _S$  . In Theorem 1.7, we describe limiting behavior of these eigenpairs on surfaces   ${S_m} \in {\mathcal {M}_{g, n}}$   when   $({S_m})$   converges to a point in   $\bar {\mathcal {M}}_{g, n}$  . Then, we consider the   $i$  th  cuspidal eigenvalue ,   ${\lambda ^c_i}(S)$  , of   $S \in {\mathcal {M}_{g, n}}$  . Since  noncuspidal  eigenfunctions ( residual eigenfunctions  or  generalized eigenfunctions ) may converge to cuspidal eigenfunctions, it is not known if   ${\lambda ^c_i}(S)$   is a continuous function. However, applying Theorem 1.7 we prove that, for all   $k \geq 2g-2$  , the sets   \[ {{\mathcal{C}_{g, n}^{\frac{1}{4}}}}(k)= \Big\{ S \in {\mathcal{M}_{g, n}}: {\lambda_k^c}(S) &gt; \tfrac{1}{4} \Big\} \]   are open and contain a neighborhood of   $\bigcup _{i=1}^n{\mathcal {M}_{0, 3}} \cup {\mathcal {M}_{g-1, 2}}$   in   $\bar {\mathcal {M}}_{g, n}$  . Moreover, using topological properties of nodal sets of  small eigenfunctions  from [ 12 ], we show that   ${{\mathcal {C}_{g, n}^{\frac {1}{4}}}}(2g-1)$   contains a neighborhood of   ${\mathcal {M}_{0, n+1}} \cup {\mathcal {M}_{g, 1}}$   in   $\bar {\mathcal {M}}_{g, n}$  . These results provide evidence in support of a conjecture of Otal and Rosas [ 13 ].

On Topological Upper-Bounds on the Number of Small Cuspidal Eigenvalues of Hyperbolic Surfaces of Finite Area