News of GCap's rejection of the offer broke at the weekend, following which its share price leapt around 50% on Monday, to close the day at just under 180p.
Yesterday they climbed another 14% to close at 205p, having reached as high as 216p during the day.
Analysts believe that Global is bound to bid higher for GCap, because Global was formed with the purpose of consolidating the radio sector.
After buying Chrysalis Radio for £170m in June it missed out on landing Emap's £400m-valued radio division at the end of 2007.
Global's offer valued the owner of Classic FM, Capital and Xfm at £310m.
It emerged yesterday that Global's advisers have started to sound out GCap's shareholders, who had not been told by the company of the offer, about their reaction to Global's approach.
Meanwhile, Emap has taken the latest step towards the completion of its break-up sale by setting the date of January 25 for the extraordinary general meeting convening its shareholders to vote for or against the £1.14bn sale of its consumer magazine and radio business to German publisher H Bauer.
The separate £1.3bn deal by which Apax and Guardian Media Group will acquire Emap after it is reduced to its business-to-business division is dependent on the positive outcome of that vote.