We study the random variable Xnk, counting the number of vertices of degree k in a randomly chosen 2-connected graph of given families. We prove a central limit theorem for Xnk with expected value EXnk ∼µkn and variance VXnk∼σk2n, both asymptotically linear in n, for both rooted and unrooted unlabelled 2-connected outerplanar or series-parallel graphs.