The authors introduce a general class of median-type filters which contain nonrecursive (finite impulse response) and/or recursive (infinite impulse response) substructures. The overall structure of the linear median hybrid (LMH) filters may be either nonrecursive or recursive. Altogether eight basic filter structures are introduced, and four of them are analyzed in more detail. General properties of the root signals, i.e. signals invariant to filtering, are discussed. Expressions characterizing the noise attenuating properties of some of the filters are derived, and a statistical analysis of the filters is performed. The LMH filters are simple structures enabling both analog and digital implementations and having properties not attainable with linear or median filters. By designing the linear substructures appropriately it is possible to tailor the root signals of the LMH filters to meet the time-domain specifications of a particular applications. >