YM and YPM are amazing in that there are almost zero other political comedies that have any life beyond a year or two. Those shows are still hilarious even 30 years later.
Last time this topic came up, someone put me on to "The Thick of It" which is quite different but also very funny. Too bad you have to subscribe to BritBox to see all of it, AFAIK.
"The Thick of it" is basically YM/YPM transposed in the modern age, namely the media/spin cycle being at the centre of politics. It's a very worth successor.
It's a _slightly_ different setup, in that Yes Minister is mostly about civil servants (the only significant civil servant character in the Thick of It is Terri); the Thick of It is mostly about political operatives (these only really show up as bit players in Yes Minister).
It perfectly satirised the government of the time. The spin doctor is one of the most powerful government figures, unelected like the civil service, and operating at the whims of the press.
"Have I Got News for You", legendary UK political satirical/comedy-panel show, 1990-still running
One thing that kept them fresh was inviting guests-of-the-hour; often beleaguered under-fire politicians, who they would then call corrupt or liars or incompetent to their faces. Not something you'd ever see on US television, other than Stewart or Colbert.
Last time this topic came up, someone put me on to "The Thick of It" which is quite different but also very funny. Too bad you have to subscribe to BritBox to see all of it, AFAIK.