Velocity and orientation measurements have been used to study the electrophoretic (1.9-22.5 V/cm) and Brownian motion of supercoiled and relaxed circular DNA (2926 and 5386 base pairs) in polyacrylamide gels (5% T, 3.3% C), using as controls linear molecules of either the same contour length or the same radius-of-gyration. Circular DNA deviate from the cyclic reptation of the linear counterparts but in a different manner at high and low field strengths because the circles tend to visit different substructures of the heterogeneous polyacrylamide gel at low and high fields. At 22.5 V/cm circles are first (within 15 ms) weakly aligned with the field by migration, before slowly (over a period of tens of seconds) becoming immobilized by impalement on protruding gel-fibers, which lead to a strongly enhanced field alignment. The rate of field-free decay for the parallel orientation is similar to that in free solution (time constants 20-40 ms, depending on DNA size), which shows that impalement occurs mainly in the more open parts of the gel. At 1.9 V/cm the circles migrate slowly and in wide zones compared to the linear form. Unexpectedly, the circles are oriented perpendicularly to the field direction, in a weak and slow manner (rise time, 50 s). The perpendicular orientation decays about 1000 times more slowly than the impalement-induced parallel orientation and furthermore is not observed in comparative experiments in agarose gels (which the paralell orientation mode is). The perpendicular mode is ascribed to a temporary squeezing of the circles against the bottom of "lobster traps" between dense regions of the polyacrylamide gel, which can be penetrated by the linear molecules but not by the circles due to DNA bending stiffness. At intermediate field strengths impaled and lobster-trapped circles exist side-by-side, as evidenced by the concomitant observation of both orientation modes. Data on the shortest pulses which detrap impaled molecules in intermittent and reversed fields, respectively, are combined to estimate the diffusion constant of circular DNA for translation off the gel fibers.