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We provide upper bounds on the degrees of the coefficients of \v{S}apovalovelements for a simple Lie algebra. If $\fg$ is a contragredient Liesuperalgebra and $\gc$ is a positive isotropic root of $\fg,$ we prove theexistence and uniqueness of the \v{S}apovalov element for $\gc$ and we obtainupper bounds on the degrees of their coefficients. For type A Lie superalgebraswe give a closed formula for \v{S}apovalov elements.  Often the coefficients of \v{S}apovalov elements are products of linearfactors, and we provide some reasons for this coming from representationtheory. We also explore the relationships between \v{S}apovalov elements comingfrom different roots, and their behavior when the Borel subalgebra is changed.

Coefficients of \v{S}apovalov elements for simple Lie algebras and contragredient Lie superalgebras