You can use Replication Manager to replicate bigdatetime and bigtime data.
Selecting bigdatetime and bigtime data for replication
On the Columns tab of the Add New Table Replication Definition dialog box, select bigdatetime or bigtime from the Replication Definition list in the Datatype area.
See “Support for bigdatetime and bigtime datatypes,” in Chapter 5, “Managing RepAgent and Supporting Adaptive Server” in the Replication Server Administration Guide Volume 1 and “Date/time, and date and time datatypes,” in Chapter 2, “Topics” in the Replication Server Reference Manual.