6 weeks is still quite a short period of time. If you are sure that this man is going to stick around, then it's all good.
But as someone who had a mum with a variety of bf's and hubbies in and out of hers and my life while growing up, I have a different perspective on things.

What is different is you are considering your children, whereas my mum just went ahead and did it, and most of the time I didn't like them, but that didn't seem to matter to anyone.

I have always said that if me and my OH split up and I was ready to date again and wanted the person to meet my kids, if my kids couldn't get on with him, then the relationship was doomed.
I know this is not thinking of me, but after my experiences growing up, I wouldn't have a man in my life that my kids didn't like.

Hopefully, your kids will like this new man. Maybe a trip out somewhere would be a good idea, somewhere on neutral ground.

All the best to you.

You are allowed friends, just like your kids are allowed friends. Start there. Introduce him in a very low key way as a friend of yours who has popped round.

My guess is they will pick up immediately that there is more to it than that. So be a bit coy and you can tell them your very fond of him and that he seems fond of you.

That way, it is less threatening than getting the whole deal all at once.

Or you could plan a night out, and say, yeah me and my friend are going to see a film... whatever....go to a concer... When they ask about it, tell them "X" is a friend.

Next step - he just happens to be staying for tea.... etc.

This worked ok with my lot.

Or you could do what my best ladyfriend did. She took her kids for a walk. Found a duck stuck in the undergrowth. Called very new b/f to come and rescue it and let her kids + new b/f do the dirty work of splashing around in the mud rescuing duck. After which they were all the best of friends, and were pleading with her to go out with him.

i'd wait six months or so. make sure that this person isn't going to come and go.
start it off as just friends.

kids are the ones who suffer when people come in and out of their lives......

there is plenty of time for the introduction.....

Wow! I felt like I was reading my own story there. I can relate to both your situation and Avalanche's answer.

I too have been seeing someone for 6 weeks with 2 busy schedules which leaves little time to spend together. The difference here is that last week he decided that he needs time to himself and now we are taking it very, very slow. I'm kind of in limbo as I don't know where I stand.

This isn't helping you I'm sure, but before he decided that he needed time, I was certain that this was going somewhere. We had talked about waiting some time before introducing the kids just to be sure that we knew that there was a future and that they could handle it. My kids have only met one guy since the separation and it was far too soon.

I think you need to feel confident that you know this is going somewhere and that your kids can handle it.

i spoke about my parner for a while b4 the kids met him this gave us all a chance to talk about tit and raise any questions.
the meeting was so succesful that i dont even remember it now every thing just kind of slotted into place

If you think in your own heart and head that this guy will stick around introduce him but as a friend then you cant go wrong let the children get to know him and see what they make of him also will give you the chance to see how he is around your kids then just go from there slowly

All great advice. The reason I asked is because, I too, had a mom - God love her - that had many men in and out of my life and living with us.... I hear that loud and clear.