In this paper, we are concerned with the Duffing oscillator, which has been applied to model many mechanical systems and has attracted much attention as a typical nonlinear system. <...> When the system is under only a harmonic excitation or random one, two popular tools used to study such a nonlinear system are the averaging method and equivalent linearization method, respectively. <...> The former was originally given by Krylov and Bogolyubov [1] and then it was developed by Bogolyubov and Mitropolskiy [2-4] and was extended to systems under a random excitation with the works of Stratonovich [5], Khasminskii [6], and others, which were reviewed in survey paper by Mitropolskiy [3], Robert and Spanos [7] and Manohar [8]. <...> The later, the stochastic equivalent linearization method, which has attracted many researchers due to its originality and capability for various applications in engineering, was first studies by Kazakov [9], who extended Krylov and Bogolyubov’s linearization technique [1] of deterministic problems to random problems. <...> This method was also reviewed in some books by Roberts and Spanos [10], and Socha [11]. <...> Recently, some approaches to the stochastic linearization have been proposed in Refs. [12-14]. <...> In [13-14], for example, Anh have proposed a dual criterion of stochastic linearization method for single and multi-degree-of-freedom nonlinear systems under white noise random excitations. <...> In a Duffing oscillator under periodic excitation, the phenomenon of subharmonic response has been known for years and has been described in many textbooks (see e.g. [15-18]) and works (see e.g. [19-21]). <...> When the system is subjected to a combination of harmonic and random excitations, however, to the authors’ knowledge, although the response of this oscillator has received a flurry of research effort for years (see e.g. [22-25]), there is no work on its subharmonic response. <...> Thus, in this research, we present a technique to treat a one third order subharmonic response of a Duffing oscillator subjected to periodic and random excitations. <...> The technique is a combination of the stochastic averaging method, the equivalent linearization method, and the technique of auxiliary function which yields the exact joint stationary probability density function (PDF) * The paper is supported by Vietnam National Foundation for Science and Technology Development <...>