We prove results about nonstandard formulas in models of Peano arithmetic which complement those of Kotlarski, Krajewski, and Lachlan in [KKL] and [L]. This enables us to characterize both recursive saturation and resplendency in terms of statements about nonstandard sentences. Specifically, a model $\mathscr{M}$ of PA is recursively saturated iff $\mathscr{M}$ is nonstandard and $\mathscr{M}$-logic is consistent.$\mathscr{M}$ is resplendent iff $\mathscr{M}$ is nonstandard, $\mathscr{M}$-logic is consistent, and every sentence $\varphi$ which is consistent in $\mathscr{M}$-logic is contained in a full satisfaction class for $\mathscr{M}$. Thus, for models of PA, recursive saturation can be expressed by a (standard) $\Sigma^1_1$-sentence and resplendency by a $\triangle^1_2$-sentence.