The directed movement into, out of or within a cell, or between cells, by means of some agent such as a transporter or pore of quaternary ammonium compounds, any compound that can be regarded as derived from ammonium hydroxide or an ammonium salt by replacement of all four hydrogen atoms of the NH4+ ion by organic groups. [ GOC:ai https://www.worldcat.org/search?q=bn%3A0198506732 ]