Parallel reductions can delete a set of black points from a binary image at a time. Parallel 2D thinning algorithms are composed of parallel reductions to produce centerlines of objects. In subfield-based parallel thinning the digital space is partitioned into \(k\ge 2\) subfields which are alternatively activated, at a given iteration step k successive parallel reductions assigned to these subfields are performed, and some black points in the active subfield are designated for deletion. A thinning algorithm is 1-attempt if whenever a border point is not deleted in the actual thinning phase, it belongs to the resulting centerline. This paper presents two subfield-based parallel thinning algorithms acting on the nonconventional hexagonal grid. It is shown that both proposed algorithms are topology-preserving and 1-attempt.