  We demonstrate that first-order phase transitions in 1+1-dimensional
nonequilibrium systems with fluctuating ordered phases are impossible, provided
that there are no additional conservation laws, long-range interactions,
macroscopic currents, or special boundary conditions. Since minority islands in
the ordered phase of such systems can only shrink by short-range interactions,
it is impossible to stabilize a fluctuating ordered state. The apparent
first-order behavior turns out to be a transient phenomenon, crossing over to a
continuous transition after very long time. As examples we consider the triplet
creation model 3X->4X, X->O, the annihilation/fission process 2X->3X, 2X->O, as
well as spreading on a diffusing background X+Y->2Y, Y->X.
