Responses at bottom:
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I have a client system administrator attempting to archive files with a command 
like:

dsmc archive '/CMS/oldpatients/039*' -subdir=y -archmc=ro_patient \ 
-description='Xio 4.51 07/19/2011 ND'

Files that are in oldpatients and have names starting with '039' get archived. 
In cases where a subdirectory of oldpatients has a name starting with '039' and 
contains one file, the subdirectory and the one file get archived. In cases 
where a subdirectory of oldpatients has a name starting with '039' and contains 
multiple files and further levels of subdirectories, neither the subdirectory 
nor any of its descendents get archived.

The system uses TSM 5.3.4.0 client code under Linux with a 2.6.9-42 kernel 
(probably RHEL 4).

Is the client supposed to behave this way? If not, is a more current client 
code level likely to help?
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If I understand your problem correctly, yes this is correct client behavior, 
and works the same in all subsequent client levels. 

This has always been a common trap, because if you look up "wildcard" in the 
client book, the first reference to it says "* is the match-all character".  
But if you keep reading, a later reference to "wildcard" says:  "In a command, 
wildcard characters can only be used in the file name or extension. They cannot 
be used to specify destination files, file systems, or directories".  So * is 
not a wildcard for matching directory names.