If you're in Version 7 or earlier, the dat.dat file is simply a text file. Consequently, you can open both dat.dat files in a text editor (Microsoft Notepad, EditPlus, or any other plain text editor will work).
First, CREATE BACKUPS of both files to make sure you can recover if you do something wrong!
Then copy the entire contents of the one file and paste it at the bottom of the other. Be careful not to include any extra blank lines between data records, and also be sure to save it in the same file format of the original files. (We occasionally see problems because people will do this on a Mac, for instance, and the format gets changed, which makes the file incompatible with SSI Web!). Save this new file as STUDYNAMEdat.dat, matching the original names of the other files.
Just a helpful hint - when I do this operation, I will often type something like XXXXXXX at the bottom of the first file before I paste in the data from the second file. Then, I can use the text editor "Find" function to find "XXXXXXX", delete it, and ensure that I've joined them correctly. Otherwise, you end up with an enormous file and have no idea where the join occurred, making it difficult to fix should problems arise!