Brothers and sisters I have none but my neice's nephew is my uncles son. Who am I?

kathy1952--

I tried this one for fun, but I couldn't nail it down completely, so I
am posting this as a comment, not an answer, unless and until you
confirm that this is the "answer" you are looking for.  My problem is
that I have not been able to confirm that a nun is an "ecclesiastic"
for the purpose of the special dictionary definition of "nephew"
(you'll see what I mean when you read my "answer").

Anyway, here's my best shot:

You are a priest who took a vow of celibacy, then fathered an
illegitimate daughter (who would be called your "niece," under a
standard dictionary definition of that term).  Your "niece" grew up
and became a nun and took a vow of celibacy, then had an illegitimate
son (her "nephew," under a dictionary definition of the term) by your
natural uncle.  Thus (even though you have no brothers or sisters) you
have a "niece," who had a baby boy by your natural uncle.  Under
standard dictionary definitions, that boy is your "niece's" "nephew"
and your uncle's "son."

The relevant American Heritage Dictionary definitions of "niece" and
"nephew" are:

Niece: "The illegitimate daughter of an ecclesiastic who has taken a
vow of celibacy."
Nephew: "The illegitimate son of an ecclesiastic who has taken a vow
of celibacy."

Source:  American Heritage Dictionary of the English Language, Fourth
Edition, Houghton Mifflin (2000)

markj-ga

This sort of riddle is very common in a form such as "Brothers and
sisters
have I none, but this man's father is my father's son."  In that
riddle, there is an answer that uses the most common definitions of
"father" and "son": the answer is that the person telling the riddle
is "this man".  The "father" need not be a father-in-law, a priest,
etc., and the son need not be anything but a regular son.

However, the only way to obtain an answer to the riddle you have posed
is to redefine "niece" from its most common definition of the
"daughter of one's brother or sister".  You need an in-law, a spouse,
a priest, or perhaps a half-sibling or adopted sibling (or some deus
ex machina) to intervene in order for the puzzle to work.

I'll just opine that since the second most common definition of
"niece" is "daughter of the brother or sister of one's spouse" (which
chesireboo appears to have hinted at), the solution to the riddle is
that the daughter of the sibling of one's spouse in turn had a sister
who had a son with one's uncle.

You are kathy1952

You are an adopted child or your brothers and sisters are deceased.

Re journalist-ga's comment:

In my view, the "adopted" solution doesn't work; once you are adopted,
you would probably think of your parents' biological children as
brothers and sisters to you.  However, I think that the "brothers and
sisters are deceased" solution is really clever.  It gets around what
had seemed to me to be the intractable problem of needing to redefine
"niece" from its most common meaning.  I suggest that journalist-ga
should be allowed to answer the question.

Or ask JustAskScott said above, you are the in-law.

You are your own Great Aunt/Uncle
If Male, you would have had to have married one of your maternal
grandparent's sisters, and vice versa, if you are female, you would
have had to marry one of your maternal granparent's brothers.

Here's a chart that will (hopefully) explain it - 

     (Your Grandparents) - (Your Great Uncle)<married>(You)
              ||
     (Your Mother aka Your Niece) - (Your Uncle (mother's brother))
              ||                                 ||
     YOU (if female)             (Your Uncle's son (aka your niece's
nephew))

Just reverse Great Uncle for Great Aunt if male.

Reminds me of the song "I Am My Own Grandpa"
http://www.geocities.com/ResearchTriangle/Forum/2288/song.html

Regards,
-flajason

I have to say I do not yet know the answer. The riddle was a challenge
from a retired police detective who is receiving radiation treatments
for cancer. It has been driving my co-workers and  me crazy. He will
tell us if we guess it right but if not we have to wait until the end
of his treatments which are about a month away. We have guessed just
about everything but not the solution proposed by flajason. I propose
this solution tomorrow and let you know if it is right. Thanks for the
help.   Kathy1952