It depends completely on how you use the results of the queries.
If you need to use the result of the first query to run the second query
then you need to define new resultsets:
$result1=mysql_query("select bla");
$result2=mysql_query("update bla");
Otherwise, you dan just re-use your old resultset, which is overwritten the next time you call mysql_query.
Small note:
If you are running many querys and you are using a new variable for each resultset, it may be advisable to use mysql_free_restult to clear the memory used for your query-results when you are finished with the data.