Hi, Carlos.

We've researched this issue and it appears that the drop down is working the following way. When the drop down is closed, because it is element that has taken the input focus, then the focus needs to be returned to the WebDropDown input. The input focus is returned with some timeout, that's why the focus on the second web drop down happens before the first drop down returns the focus to its input. In that case it is 100 ms. Removing the timeout is not appropriate solution, cause the control depends on it in some cases. That's why the only possible workaround is manually setting the focus to the second drop down. I'm attaching sample with solution, that contains the following code:
 
dd1_Opened = false;
dd2_Focused = false;
function WebDropDown1_DropDownOpened(sender, eventArgs) {
    dd1_Opened = true;
}
function WebDropDown1_DropDownClosed(sender, eventArgs) {
    if (dd1_Opened && dd2_Focused) {
           $find("WebDropDown2")._elements.Input.focus();
       }
       dd1_Opened = false;
       dd2_Focused = false;
}
function WebDropDown2_Focus(sender, eventArgs) {
      dd2_Focused = true;
}

Thank you for the cooperation and for using our product.

Best regards,

Nikolay Alipiev

Software Developer