This is a comparative study of The Importance of Being Earnest by Oscar Wilde and Travesties by Tom Stoppard, the two representative plays of the two great dramatists, attempting to analyze three shared characteristics of the two plays, i.e., paradox, parody and self-consciousness. Through the comparison, Wilde’s influence on Stoppard is highlighted.First, both Wilde and Stoppard demonstrate a penchant for paradox. For them, paradox is not only a form of witticism, but also a strategy to reverse the relationship between binary oppositions, and a strategy to subvert the conventional and established concepts and notions. The discussion highlights a vital paradox, "life holds the mirror up to Art." This inversion of the relationship between life and art reflects Wilde’s art for art’s sake aesthetic doctrine and proves that Stoppard is an inheritor in this respect. Two other issues, contradiction embodied in paradoxes, and the connection between marginality (non-Englishness) and paradox are discussed. The two features are driving forces behind both Wilde’s and Stoppard’s paradoxes.Secondly, both Wilde and Stoppard are famous parodists. They keep a dialectic stance in dealing with the convention, remove its stale elements and retain its viable ones. For this end, parody serves as a perfect device. By applying it, both playwrights are able to deliberately mine the dramatic conventions and assimilate popular forms into their dramaturgy. This reflects a spirit of self-consciousness. It is self-consciousness that carries weight behind both paradoxes and parody in Wilde and Stoppard’s plays. Fundamentally, self-consciousness is an embodiment of a critical spirit in a broader sense, which is borne by Wilde and Stoppard alike. In paradoxes, both writers employ this self-consciousness to criticize various established concepts and norms. In parody, they self-consciously criticize the dramatic conventions and popular forms. They demonstrate this self-consciousness in self-criticism with regard to the role and functions of art and artist. Indeed, it is with this self-consciousness that both playwrights have executed a combination of creation and criticism. And it is this combination that distinguishes Wilde and Stoppard from lesser dramatists or critics, and it is this combination that establishes their fame and influence both in drama and in criticism.