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U heard it right, u can check it thru internet..but u must know arabic,,it is under services,,electronic,,,u have to put the application number and company computer no....if its under personel u have to put qatar id number. use the following link
when u get page 1st radio button is for company
second one is for personal visa tracking... then click on right side tab to see the status..ok
go to www.mlsa.gov.qa and check under 'electronic services' column.
But the entire website is in arabic as the english version is under construction. So take the help of any arabic speaking mate of yourself and find out.
they take mini time 4days and maxi 1month.
go to WWW.MOI.GOV.QA and click on the visa application/visa tracking section