How do I tell the Access 2003 package wizard to run additional install programs (.exe or .bat)?

From the extentions Help - as good as anything I could write for you ;-)

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The Setup.exe file used in your package is copied from your Microsoft Office 2003 CD. The Setup.ini files contains the settings that Setup.exe uses during the installation of your application, including the following settings:

Name/Product Code/location of <PARENT>.MSI
Minimum operating system and System Pack requirements
Display Mode
Details of each subsequent chained install
Log file folder
Any chained executable files (for example, .vbs, .exe, or .reg files)
Setup.ini also provides a convenient way to link multiple .msi files in a given installation.

For each chained file, include a [ChainedInstall_i] section. To avoid unpredictable behavior, ensure that you number chained installations in sequence, for example, [ChainedInstall_1], [ChainedInstall_2], and so forth. Specify the relative path to Setup.exe of the .msi file that you want to install.

The section specifying a linked .msi file may appear in the Setup.ini as follows:
[ChainedInstall_1]
Path="\Files\ACCESSRT.MSI"
TaskType=MSI
CmdLine=/qf \

Note  You can also link executable files, such as .bat, .vbs, .reg, .exe files. When linking executables, specify "EXE" as the TaskType in Setup.ini.
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I'll need a little more handholding on this one.

What would my .ini file look like? Let's assume that I want the file OtherSetup.exe to run after the Access files have been installed. Here's my current setup.ini file (I've deleted the comments from the file). What would the revised setup.ini file look like?

; SETUP.EXE settings file.
[MSI]
MSI=\Files\myPgm.msi
[Product]
ProductCode={my product code number goes here}
ProductName=MyAccessProgram
ProductVersion=0.81.0000
SkipLangCheck=1
[Display]
Display=full
CompletionNotice=Yes
[Logging]
[MinOSRequirement]
VersionNT_1=500
WindowsBuild_1=2195
ServicePackLevel_1=3
[Cache]

Your solution almost works. The installer installs the Access files. Then it looks for the tamrun11.exe file.

But the installer cannot find the tamrun11.exe file. The package wizard does not put the tamrun11.exe file into the Files folder as a separate file. I guess it must be integrated into the .msi file.

Is there a way to reference tamrun11.exe properly when it is in the .msi file--or do I have to manually place it into the Files folder as a separate file? It's not a big hassle having to do it. But if I don't have to do it, that would be nice.

What had you done with the exe file up to that point?
If you've got the line
Path="\Files\tamrun11.EXE"
in your ini file - then you'll need to make sure that tamrun11.EXE is in place as specified.

There's no automated way of putting it there - as you're editting the ini file manually :-)

I had told the Access package wizard to include the tamrun11.exe file--and some other additional files. The installer correctly copies these files to the \Program Files\MyAccessProgram folder along with MyAccessProgram.mde.

These additional files, however, are nowhere to be found on the installation CD that I create. That's why I am guessing that they are integrated into the .msi file on the installation CD.

It sounds like you are saying I cannot set the Path to something like Path="\Files\MyPgm.msi\tamrun11.exe". Instead, I have to put tamrun11.exe into the Files folder. Is that what you are saying?

Yeah - that's where I'd always look to put it.

It works, now. Thanks very much!

Welcome.  Glad you're sorted :-)