Is it valid to have a html form inside another html form?

A. It is not valid HTML nor XHTML

In the official W3C XHTML specification, Section B. "Element Prohibitions", states that:

"form must not contain other form elements."

http://www.w3.org/TR/xhtml1/#prohibitions

As for the older HTML 3.2 spec, the section on the FORMS element states that:

"Every form must be enclosed within a FORM element. There can be several forms in a single document, but the FORM element can't be nested."

B. The Workaround

There are workarounds using JavaScript without needing to nest form tags.

"How to create a nested form." (despite title this is not nested form tags, but a JavaScript workaround).

Answers to this StackOverflow question

Note: Although one can trick the W3C Validators to pass a page by manipulating the DOM via scripting, it's still not legal HTML. The problem with using such approaches is that the behavior of your code is now not guaranteed across browsers. (since it's not standard)

In case someone find this post here is a great solution without the need of JS. Use two submit buttons with different name attributes check in your server language which submit button was pressed cause only one of them will be sent to the server.

<form method="post" action="ServerFileToExecute.php">
    <input type="submit" name="save" value="Click here to save" />
    <input type="submit" name="delete" value="Click here to delete" />
</form>

The server side could look something like this if you use php:

<?php
    if(isset($_POST['save']))
        echo "Stored!";
    else if(isset($_POST['delete']))
        echo "Deleted!";
    else
        echo "Action is missing!";
?>