We establish a strong maximum principle for a nonnegative continuous solution den">de"> of a doubly nonlinear parabolic problem in a space–time cylinder Ω×(0,τ)den">de"> with a domain Ω⊂RNden">de"> and a sufficiently short time interval (0,τ)⊂(0,T)den">de">. Our method takes advantage of a nonnegative subsolution derived from an expanding spherical wave.