Where did they go? I saved my game a few times but the next time I went to play... I have no saved games...

Did you change compatibility mode or anything like that?

I'm just running it on Vista 64 in the DOS box that came with the game. Just installed and played, and it wont save my game.

Have you started a new game with more than one player name ?
Saves are bound to the player name you choose IIRC...
Cycle through the available players to see if the saves turn up...
If it's really not saving at all, try to run the game as admin, as Ralackk suggested, or installing to a directory other than the deafult 'Program Files'...

Okay, so I ran it as admin, and I also deleted the generic "EASY" player name that it came with and now I am able to save my games, I'm not sure which one worked for sure, but I appreciate the help. Thank you.

Ok, good to know.
Go ahead and mark Ralackk's post as the solution, since it was probably not running it as admin that was keeping you from being able to save.
Have fun ;)

I just started up the game for the first time (win 7 pro 32) and had this same issue, the save files are on my PC still, just in a weird folder. Mine were in

c:\users\Don\appdata\local\virtualstore\program files\gog.com\under a killing moon

I copied and pasted them back to the right folder and away she goes

Any idea what this second "ghost" copy of all the data is?

That's the default directory Vista and Win7 sometimes redirect savegames to when stuff installed to Program Files is not run as Admin. If, right after installing the game, you tick the 'Run as Admin' checkbox on the shortcut before you start playing most likely saves are stored right from the start on the game folder and the Virtual Store folder is never used.

Tried all of the above.Unable to save any gog games unfortunately. Running as admin (both pre ticked and right clicking on each play). win 7 64 bit. any other ideas greatly appreciated

I'm not sure what else to suggest. Maybe try to temporarily disable UAC ?

The: Run as an admin idea did work for me. :) finally I can play and save the Tex Murphy Games again. :)

I had the same problem, not having any saved games work. Running as an administrator solved the problem for me, as well. I know this is an old thread, but my thanks to those who offered up this solution.