Given that the dynamics, or time-evolution, of the ferromagnetic properties of thin films has generated an enormous literature, it is surprising that a fundamental dynamical property such as critical slowing down near a phase transition has hardly been investigated experimentally. In the context of ferromagnetism, critical slowing down refers to the prediction that the relaxation of the magnetization toward equilibrium occurs more and more slowly as the temperature, Tc, of a phase transition is approached. The relaxation time is predicted to scale as a power law in (T-Tc)/Tc with dynamical exponent z, essentially because the size of the magnetically correlated regions grow like a power law near Tc. Although this theoretical description of a phase transition was worked out starting in the 1960s, the measurement of the dynamical critical exponent has proven to be very difficult, even for a conceptually simple system like the two-dimensional Ising model. We have recently approached this problem through the first studies of critical slowing down in ultrathin ferromagnetic films. By measuring the magnetic susceptibility of Fe/W(110) near the Curie temperature, we are able to determine the dynamical critical exponent for the 2D Ising model in an internally consistent manner.