We study the time dependent magnetic behavior of uniaxial cobalt films in the vicinity of the dynamic phase transition (DPT) as a function of the period P and bias H(b) of an oscillating magnetic field. In addition to the DPT at a critical period P(c), we observe the occurrence of transient behavior for P<P(c). Our data can be consistently explained by the existence of a phase line at H(b)=0 for P<P(c), which causes a first order phase transition in between two antiparallel dynamic order states, thus indicating far-reaching similarities of the DPT to equilibrium phase transitions in ferromagnets.