A B757 crew declared an emergency and deviated around weather on an oceanic route after being denied clearance for the deviation due to traffic.

Narrative

While at level cruise flight 33000 FT flight was proceeding on assigned route when we approached a line of embedded thunderstorms. The weather was about 85 to 100 NM directly in front along the route of flight. The storms were approximately 75 NM wide with tops at 37000 FT. We contacted the commercial radio server via HF radio to request deviation around the weather. I initially requested a left deviation 50 miles and was denied. I then requested a right deviation 75 miles and was denied a second time due to traffic. At that time; I informed the commercial radio server that I was using Captains' authority and declaring an emergency to avoid the weather. I told the commercial radio server I was going to proceed right of course 75 NM. Commercial radio server then phone patched us directly to ATC. We were about to climb 500 FT when ATC cleared us to climb to 34000 FT. ATC initially queried us why we did not declare an emergency; and I informed him we did with and he acknowledged that we had as he received confirmation on his screen. After we declared an emergency; the commercial radio server said we can proceed 50 NM right of track; however we need approximately 75 NM right in order to clear the weather and told commercial radio so; and they acknowledged. Once we cleared the weather; we reported back on course and the remainder of the flight was uneventful.