  The consequence of dynamical mass generation on the singularity structure of
propagators is discussed. First the phenomena of dynamical mass generation is
discussed in the framework of Euclidean gap equations, then a possible
Minkowski solution is looking for. The examples are reviewed and studied for
several models: Yukawa, QED, QCD and Wess-Zumino. It is argued that the absence
of propagator pole goes hand by hand with the nontrivial solution for mass
function. The consequences are discussed.
