Alexander Koryagin:

AS>> I will have him repair my car. (1)
AK>
AK> "Repair" is a verb, and you use the direct object here.
AK> And therefore you had to use "to" before the verb.

No, I hand't.  This usage needs the bare infinitive.

AK> "He asked me to wait a little".

You ask someome to do something, but you have someone do it.
There is a qulitative difference between /ask/ and /have/.

AS>> You may call it a past participal in the second
AS>> instance, because it partakes of the verb, or, is
AS>> partially a verb.
AK>
AK> I don't understand your logic here.

Have you wondered why it is called participle?  What
definition of participle do you use?  Here is the one I use,
by Goold Brown --

   A Participle is a word derived from a verb,
   participating the properties of a verb, and of an
   adjective or a noun; and is generally formed by adding
   /ing/, /d/, or /ed/, to the verb: thus, from the verb
   rule, are formed three participles, two simple and one
   compound; as, 1. /ruling/, 2. /ruled/, 3. /having
   ruled/.

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