Various special families of polynomials satisfy a differential-difference equation of the form Pn+1(x)= An(x)P′ n(x)+ Bn(x)Pn(x),where An and Bn are polynomials of degree at most 2 and 1 respectively.We investigate the asymptotic distribution of the zeros of Pn in case the zeros are real and interlacing with those of Pn-1 and the polynomials An and Bn converge,possibly after some scaling.It turns out that the asymptotic zero distribution has a Stieltjes transform that satisfies a differential equation of Riccati or Abel(of the second kind).We illustrate our result using various examples: the classical orthogonal polynomials of Hermite,Laguerre and Jacobi,but also some families of non-orthogonal polynomials such as the Bell polynomials,tangent polynomials and inverse error function polynomials.