Making use of generalized bivariate Fibonacci polynomials, we propose two families of regular functions of the type ϕ(ζ)=ζ+∑j=2∞djζj, which are bi-univalent in the disc {ζ∈C:|ζ|<1} involving the (p, q)-derivative operator. We find estimates on the coefficients |d2|, |d3| and the of Fekete–Szegö functional for members of these families. Relevant connections to the existing results and new consequences of the main result are presented.