  Let $(M,g)$ be a Zoll manifold, i.e., a smooth, compact, Riemannian manifold
without boundary all of whose geodesics are closed with a minimal common period
$T$. The positive definite Laplace-Beltrami operator has eigenvalues
$\{\lambda_j^2\}_j$ which cluster around $\nu^2_\ell$ for some sequence
$\nu_\ell\to \infty$. This article is concerned with the number of $\lambda_j$
in a window of fixed size $\mathrm{w}$ around $\nu_\ell$, denoted by
$\mathbf{N}(\nu_\ell,\mathrm{w}):=\#\{j\,:\,
\lambda_j\in[\nu_\ell-\mathrm{w},\nu_\ell+\mathrm{w}]\}.$ When the set of
trajectories with period smaller than $T$ has zero measure, there is $c_{n}>0$,
depending only on $n=\operatorname{dim} M$, such that $$
\mathbf{N}(\nu_\ell,\mathrm{w})
=c_n\operatorname{vol}_g(M)\nu_{\ell}^{n-1}+o(\nu_{\ell}^{n-1}), $$ as $\ell
\to \infty$. However, for a general Zoll manifold this may not be the case. We
show that, nevertheless, there is $N>0$, independent of $\ell$, such that $$
\sum_{j=0}^{N-1}\mathbf{N}(\nu_{\ell+j},\mathrm{w})=
c_nN\operatorname{vol}_g(M)\nu_{\ell}^{n-1}+o(\nu_{\ell}^{n-1}), $$ as $\ell
\to \infty$. In addition to asymptotics for the counting function, we study the
kernel of the spectral projector for the Laplacian,
$\Pi_{\ell,\mathrm{w}}(x,y)$ onto the spectrum in
${\bigcup_{j=0}^{N-1}[\nu_{\ell+j}-\mathrm{w},\nu_{\ell+j}+\mathrm{w}]}$. We
show that for $x$ and $y$ in a shrinking neighborhood of a point with few loops
of length smaller than $T$, $\Pi_{\ell,\mathrm{w}}(x,y)$ and its derivatives
have the same asymptotics as those on the round sphere and flat torus.
