It's 1.a8=B, then keep the close opposition if 1...Ke8 or Kg8, then whatever move, 2.b8=Q# or b8=R#.
BUT (and this is really amazing), the catch is if black plays 1...Kf8 and that's why you have to on 1st move promote to bishop instead of knight (promoting to rook or queen would be stalemate), so you can on 2nd move promote b-pawn to queen or rook, then black plays 2...Kf7, and 3.Bd5# is mate. Rooperi, where do you find these Loyd's puzzles?!
Ah well done! Great puzzle, isnt it?
I have a collection of 332 Loyd Problems.
There is a little application you can download, called PROBLEMISTE. You can download a shareware version here: http://www.problemist.com/
There are huge collections and anthologies by many composers, I must have 250 000 problems. (including helpmates etc)
It is also very helpful to check my own compositions for flaws, and it has a search function, which is useful for catching out people trying to pass off someone else's work as their own : )
One More!
S. LOYD
New York Albion 1858 Mate in 3
Qh1+ Kxh1 Rxb4 Bh2 Rxc7 hoo rargh!
Qh1+ Kxh1 Rxb4 Bh2 Rxc7 hoo rargh!
And after Qh1 Kg3?
i believe Qh1 Kg3 Qf3+ Kh2 Nxb4 mate. Or Qh1 Kg3 Qf3+ Kh4 Qxb4 mate.
Perfect!
And another, mate in 5. This one is quite famous....
I tried different things, but it's clear that both rooks must stay on their ranks, so that everything is forced. If you look at the position you can see the pattern with rook-pawn on 7th rank and king in the corner next to the pawn. So the idea is to get your king to f2 and then give check. This would be mate, since king is stalemated.
First move is 1.Rf2, this prepares black's Bxf2, but now bishop is still pinned. Black's only response is 1...a4. Then 2.Kd2 to get king closer and keep 1st rank free for the rook (not 2.Kd1). Black plays 2...a3. Next move is 3.Ra1 to block black's a-pawn and prepare next move. Black's only response is 3...a2. Then 4.Ke1, this frees black's bishop from pin, so again black has only one move to make - 4...Bxf2. And then... 5.Kxf2#
Rooperi, thank you for your information on the Problemist. The problem above is similar to the 6th and 14th problem in Loyd's collection (I haven't made it much further yet) - again, there are only few pieces on the board and the mate is quite similar, but it's much more easier (both mate in 2):
Showing you in diagram:
Well done...
The first one in post 32 may be 1.Qa1 where
1... N(anywhere) or 1...g5 2.Kc7#
1...Bg8 2.Kxg6#
1...Kg8 2.Qxa8#
For the second, 1.Kf5 looks good.
1...Kxd5 2.Qd1#
1...Kd7 2.Ke5#
Nice two-movers.
Mate in two moves:
(Rooperi, I hope you won't feel that I'm stealing your thread from you, but this one is quite nice. Thank you again for the Problemist, it's great!)
1.Re1
1...Kxe1 Qd2#
1...Be2 Qg1#
1...Bg2 Qh4#
Hey, go ahead.... 
SirDavid, that's correct. Here's another one, mate in two moves:
Thanks for the puzzles... that 3rd one was absolutely sick! 
and everyone after that made me cry a little.
Bc8, seen this one before posted already.
OK, one more, Mate in 3