Two equations describing past marginally trapped surfaces in twisting algebraically special space-times are obtained. One of them generalizes the equation discussed by Tod for twist-free (Robinson-Trautman) metrics. The second one is solvable under certain algebraic conditions, closely related to "m > 0" and "m(2) > a(2)" of the Kerr metric. Consequences of the existence of a null horizon are discussed. Kerr-Schild metrics admitting such horizons are shown to be of Petrov- type D. (C) 2010 American Institute of Physics. [doi:10.1063/1.3511331]