In the paper, a characterization of simple period doubling points of a discrete dynamical systemxk:+l=f(xk, λ)f:ℝn× ℝ → ℝnby a set of singularity and nondegeneracy conditions is given. These conditions reduce to those given in the book of Gucken-heimer/Holmes [83] for the scalar casen= 1. Based on this characterization, a minimally extended systemG(x, λ) = 0 for defining period doubling points is proposed.Itconsists of the fixed point equationf(x, λ)−x= 0 and a certain singularity conditiong(x, λ) = 0g: ℝn× ℝ → ℝnMoreover, an analogously constructed minimally extended system for pitchfork bifurcation points is given, and the relation between pitchfork bifurcation and period doubling points is discussed. The minimally extended system is used for computing period doubling points by Newton-type methods. The solution of the linear systems required in Newton's method is realized by a block elimination technique similar to that introduced by PÖNisch/Schwetlick [81]. The performance of the algorithm is demonstrated on hand of a periodically excited Duffing oscillator where the Feigenbaum sequence of period doubling points is computed up to period 32