Salesmen "make the rounds" to sell their products and the periods of sale are often called a "round of sales." I understand the sentence to say, "What are the deadlines (or due dates) for the sales rounds (or periods) for the various (or different) markets."

First round of sales due: September 3, 2003
http://www.pack936.org/popcorn.htm

GENEVA, Switzerland -- Tickets for the 2008 European Championship finals were 30 times oversubscribed after seats went on sale in the first round of applications, European soccer's governing body UEFA said on Monday.
The huge demand means the second **round of sales** -- initially planned to allocate unsold tickets on a first come, first served basis in June -- has been abandoned and will be replaced by a lottery.
Almost 600,000 fans from 142 countries had ordered 10.4 million tickets when the deadline expired on March 31 -- 18 times more than for the Euro 2004 finals in Portugal and almost as many as for last year's World Cup in Germany.
http://edition.cnn.com/2007/SPORT/football/04/02/uefa.cup/

Soccer fans placed some 677,900 orders for a total of six million tickets in the sales period from December 12 to January 15. There are only 250,000 tickets available from this third and final major **sales period.**
In the first two **sales rounds**, 812,000 tickets were sold. They were 12 times oversubscribed.
http://www.boston.com/sports/soccer/articles/2006/01/16/huge...

A huge thanks to all who made purchases during the spring flower sale held by the Program for Health Care to Underserved Populations (PHCUP)… Thanks again to all who bought flowers during this past sale. Look for our next **round of sales** in the fall.
http://www.dgim.pitt.edu/DGIM_news/info.asp?id=113&issue_mon...

[salesmen make rounds]
The salesmen (called "drummers") would rent a horse and buggy from the livery stable behind the six-room hotel to make their rounds.
http://seiz2day.com/lakeviewny/lakeviewphotos.htm

and the salesmen still make their rounds.
http://c2.com/cgi/wiki?IsComputerScience

salesmen must make the rounds once every few weeks instead of annually
http://www.time.com/time/printout/0,8816,849344,00.html


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Note added at 5 days (2007-12-07 16:41:59 GMT) Post-grading
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You're welcome, msabeh, and thank you :-)