Abstract : We introduce and investigate two new subclasses 𝒩 Σ δ, μ n, α, λ and 𝒩 Σ δ, μ n, β, λ of analytic and bi-univalent functions in the open unit disk 𝕌 . For functions belonging to these classes, we obtain estimates on the first two Taylor-Maclaurin coefficients a 2 and a 3 .