Is intraday stock trading in U.S listed exchanges from India illegal?


I have come to know about few firms in India that offers to trade in U.S stock exchanges (NYSE, NASDAQ, AMEX) from India. I would like to know; is all this legal? I've met some traders from those firms also. However, they all seem to not know about this.

Please help me and let me know if it is legal or illegal from Indian government, SEBI and RBI's perspective.

as far as i know, intraday trading comes under speculation and hence is not allowed. But i think delivery is allowed. Yes i have seen a broker offering this.
I feel it works in a complicated sense.
First of all, you cannot get a demat account in US unless you are working there or you have a green card from there.
There are Indian born people who have permanent US visas and they can trade in NYSE etc. These non residing Indians probably run business from US. What they do is, through their relatives here in India they open up a trading firm. You invest your money with this Indian trading firm and they forward the information to the US based Indians. But they do not send your money there. The US based Indians invest their money back in NYSE etc and trade as you direct. They somehow balance out the cash flow between the two countries.