Fuse size for dual amps

[ailee]

I currently have a 4 channel amp powering my speakers in my car. I am planning on getting a 12" sub and an amp to power it. I have a 4 gauge wire run all the way to the trunk for my current amp. I am going to get a distribution block and run the 4 gauge wire to the block and 8 gauge wire from the block to each amp. My question is how do I go about determining what size fuse to use. I already have a 60amp fuse for the current amp and I'm not sure what size fuse I will need to replace it with. The new amp will most likely need a 60amp fuse as well so do I run a 120 amp fuse or keep my 60 amp fuse. I'm pretty sure I just need to run a single 60 amp fuse but I want to make sure before I start buying stuff. Thanks.