I wouldn't, simply because it'd take more time in the long run. Stick with one, get a grasp on it, then move to the other. It's quicker to tackle one thing at a time than two things at a time.

It's really up to you, everyone learns differently. For you it may help you learn faster. Personally, I don't know ActionScript so I can't attest to their similarity. With PHP having so many built-in functions and a pretty short learning curve, after you learn the basic syntax you can always refer to php.net for a function.

I think that when you have skills with a programming language, it is much easier to learn another one. But probably it is hard to learn more than one language simultaneously.
As to me, I'm a Delphi developer with more than 5 years of experience and I also worked with PHP, VBA, and little with C#. BTW, I really like PHP as it is quite easy yet powerful.

Sincerely,
Tom Barnett
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I find that initial learning period frustrating when you aren't quite sure how things work and you are regualrly going to the manual to look up the syntax. I suppose if you were almost doing it like a research study and taking two fairly similar languages (PHP and ASP?) and then taking the time to document the comparison and differences it might be quicker in the end than taking them one at a time. That would take some patience. You'd have to be prepared to work on small examples in both languages for quite a while and not be in a rush to do a project with either one. Unless I was planning to write a book and document what I had learned, I'd find this pretty tedious. If you are more of an academic, you might be able to handle it.