=OR(condition1,condition2)
will give a result of "true" if either condition is true or "False" if both conditions are false
So use =If([red]OR(Mydate=<1Sept2006,Mydate>=1May2007)[/red],"Yes","No")
Dates are held in Excel as numbers. And the above won't quite work as written.
The easiest way to specify 1Sept2006 is to enter it into another cell and then refer to that cell in your OR formula.
If([red]OR(Mydate=<$A$1,Mydate>=$A$2)[/red],"Yes","No")
Gavin