  The first study of resonances in $^{17}$O+$\alpha$ elastic scattering was
carried out using the Thick Target Inverse Kinematics (TTIK) method. The data
were analyzed in the framework of an $\textit{R}$-matrix approach. Many
$\alpha$-cluster states were found in the $^{21}$Ne excitation region of the
9-13 MeV excitation energy including the first observation of a broad
$\textit{l}$=0 state in an odd-even nucleus, which is likely the analog of the
broad 0$^+$ at 8 MeV in $^{20}$Ne. The observed structure in $^{21}$Ne appeared
to be strikingly similar to that in $^{20}$Ne populated in the resonance
$^{16}$O+$\alpha$ scattering. The results are also useful for refinement of
data on an $^{17}$O($\alpha$,$\textit{n}$) reaction important for astrophysics.
