In this paper, we focus on the admissible transcendental meromorphic solutions of the following delay Schwarzian differential equations with rational coefficients \(f(z+1)-f(z-1)+a(z)S(f,z)={{P(z, f(z))} \over {Q(z, f(z))}}.\) We obtain the necessary conditions on the degree of R(z, f) for these delay differential equations and give a classification of the delay Schwarzian differential equations according to the multiplicities of the root of Q(z, f) on f. Finally, we provide some examples to illustrate that all cases occur.
