  We study Seshadri constants of ample line bundles on hyperelliptic surfaces.
We obtain new lower bounds and compute the exact values of Seshadri constants
in some cases. Our approach uses results of F. Serrano (1990), B. Harboune and
J. Roe (2008), F. Bastianelli (2009), A.L. Knutsen, W. Syzdek and T. Szemberg
(2009).
