  The total energies and various bound state properties of the excited $2^1S(L
= 0)-$states in two-electron helium atoms, including the ${}^{\infty}$He,
${}^4$He and ${}^3$He atoms, are determined to very high numerical accuracy.
The convergence of the results obtained for some electron-nuclear and
electron-electron expectation values and, in particular, for the
electron-nuclear and electron-electron cusp values, is discussed. The field
component of the isotope shift and lowest order QED correction are estimated
for the $2^1S(L = 0)-$states in the ${}^4$He and ${}^3$He atoms. We also apply
our highly accurate methods to numerical computations of the excited
$n^1S-$states (for $n$ = 3 and 4) in two-electron atomic systems.
