Wavefront dislocations-i.e. singularities of the phase of a wave psi in the form of moving lines in space where mod psi mod vanishes-are studied for initially plane waves that have passed through a random space and time-dependent phase-changing screen. For transmitted waves that are Gaussian random, incoherent, quasi-monochromatic and paraxial the following quantities are calculated in terms of the statistics of the phase screen: dislocation densities, i.e. the average number of dislocation lines piercing unit area of variously-oriented surfaces, and dislocation fluxes, i.e. the average number of dislocation lines crossing unit length of variously-directed lines in unit time.