Good start. I hope Kagome gives him a hard time. Keep up the good work & please update soon:)

The plot is good, the spelling & in some cases word choice needs work. Summary: Sesshomaru mated with Kagome after the battle with Naraku, for the sole purpose of having an heir with both spiritual and demonic powers. After half a century he took a demoness as his mate. It would be a good idea to run it through a spell-checker, you seem to have a problem with spelling century correctly & in a few places you have excess words that mess up the sentence like in the 1st paragraph you have 'the demon Slayer followed the monk after a few months after his death.' It would read better if it was something like; the demon Slayer followed (or joined) the monk a few months after his death.

Love it! Way better here than on ff.net, though your spelling and grammar still needs help. Should I beta for you?

oooh drama, haha kagome had better not sesshoumaru so quickly back... her fiery personality should be showing...haha

I can't wait to see what happens next in chapter 2,serves Sesshomaru right if Kagome refuses to talk to him lol.