  We provide upper bounds on the degrees of the coefficients of \v{S}apovalov
elements for a simple Lie algebra. If $\fg$ is a contragredient Lie
superalgebra and $\gc$ is a positive isotropic root of $\fg,$ we prove the
existence and uniqueness of the \v{S}apovalov element for $\gc$ and we obtain
upper bounds on the degrees of their coefficients. For type A Lie superalgebras
we give a closed formula for \v{S}apovalov elements.
  Often the coefficients of \v{S}apovalov elements are products of linear
factors, and we provide some reasons for this coming from representation
theory. We also explore the relationships between \v{S}apovalov elements coming
from different roots, and their behavior when the Borel subalgebra is changed.

Representation Theory