In this paper a unique continuation theorem for solutions of the porous medium equation (in one space dimension) near the free boundary is proved. In addition, by means of a Cauchy-Kovalevski type argument, a local existence theorem is proved, which says that for any real analytic curve \(x=\zeta (t)\), with \(\zeta '(t)>0\), there exists a solution of the PME, defined in a neighbourhood of the given curve, which has this curve as free boundary.