  The main purpose of this article is to show that every commuting Jordan
derivation on triangular rings (unital or not) is identically zero. Using this
result, we prove that if $\mathcal{A}$ is a 2-torsion free ring such that it is
either semiprime or satisfies Condition (P), then every commuting Jordan
derivation from $\mathcal{A}$ into itself, under certain conditions, is
identically zero.
