  The spectral properties of a singular left-definite Sturm-Liouville operator
$JA$ are investigated and described via the properties of the corresponding
right-definite selfadjoint counterpart $A$ which is obtained by substituting
the indefinite weight function by its absolute value. The spectrum of the
$J$-selfadjoint operator $JA$ is real and it follows that an interval
$(a,b)\subset\mathbb R^+$ is a gap in the essential spectrum of $A$ if and only
if both intervals $(-b,-a)$ and $(a,b)$ are gaps in the essential spectrum of
the $J$-selfadjoint operator $JA$. As one of the main results it is shown that
the number of eigenvalues of $JA$ in $(-b,-a) \cup (a,b)$ differs at most by
three of the number of eigenvalues of $A$ in the gap $(a,b)$; as a byproduct
results on the accumulation of eigenvalues of singular left-definite
Sturm-Liouville operators are obtained. Furthermore, left-definite problems
with symmetric and periodic coefficients are treated, and several examples are
included to illustrate the general results.
