"His suspicion that she was unfaithful
His doubt that she would be there"

The 'that' clauses here are noun complements: they specify what the 
suspicion and doubt are, respectively. Again, the existence of some kind 
of suspicion or doubt is in the semantics of each derived nominal, just 
as "eat" has a non-specfic "eatee" in its semantics.

They aren't appositives. I would not necessarily analyse them as 
relative clauses, either, though some people (maybe even most) would. 
This is just another function, like direct object. Again, various 
constructions can be noun complements: "a book about Donald Trump", "the 
history of Troy" have PP complements, for ex.

This explanation may be too advanced for the grammar novice, however.
-- 
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Johanna Rubba   Associate Professor, Linguistics
English Department, California Polytechnic State University
One Grand Avenue  • San Luis Obispo, CA 93407
Tel. (805)-756-2184  •  Fax: (805)-756-6374 • Dept. Phone.  756-2596
• E-mail: [log in to unmask] •      Home page: 
http://www.cla.calpoly.edu/~jrubba
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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