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Sufficiency criteria are established to ensure the asymptotic stability and boundedness of solutions to third-order nonlinear delay differential equations of the form \begin{equation*} \begin{array}{c} \dddot{x}(t)+e(x(t),\dot{x}(t),\ddot{x}(t))\ddot{x}(t)+g(x(t-r),\dot{x} (t-r))+\psi (x(t-r)) \\ =p(t,x(t),x(t-r),x^{\prime }(t),x^{\prime }(t-r),x^{\prime \prime }(t)). \end{array} \end{equation*} By using Lyapunov's functional approach, we obtain two new results on the subject, which include and improve some related results in the relevant literature. Two examples are also given to illustrate the importance of results obtained.