  We compare two different constructions of higher dimensional parallel
transport. On the one hand, there is the two dimensional parallel transport
associated to 2-connections on 2-bundles studied by Baez-Schreiber, Faria
Martins-Picken and Schreiber-Waldorf. On the other hand, there are the higher
holonomies associated to flat superconnections as studied by Igusa, Block-Smith
and Arias Abad-Schaetz. We first explain how by truncating the latter
construction one obtains examples of the former. Then we prove that the
2-dimensional holonomies provided by the two approaches coincide.
