From time to time very slow UPDATE

I have a system:
Windows XP SP2
MySQL 5.0.27
PHP 5.2.0 (mysqli ext)

CREATE TABLE parts ( partid int(10) unsigned NOT NULL auto_increment, oenumsearch char(30) NOT NULL, tmid smallint(5) unsigned NOT NULL default ‘0’, oenum char(35) NOT NULL, isset smallint(5) unsigned default ‘0’, numtypeid smallint(5) unsigned default ‘0’, textid int(10) unsigned default NULL, texts char(255) default NULL, isttx tinyint(1) unsigned NOT NULL default ‘0’, isimg tinyint(1) unsigned NOT NULL default ‘0’, isauto tinyint(1) unsigned NOT NULL default ‘0’, remarks char(255) default NULL, PRIMARY KEY (partid), KEY tmid (tmid), KEY oenums (oenumsearch,tmid), KEY oenumsearch (oenumsearch), KEY isset (isset), KEY numtypeid (numtypeid), KEY textid (textid) ) ENGINE=InnoDB

I start transaction and update some tables. One of the updated tables is parts. When start query:

UPDATE parts SET textid=1471, texts=“Some text” WHERE partid=47437

Database is stuck, and query executed about 300-400 seconds. In this time I cant start another query. Another query is wait while ends query for update.
This stuks is happend form time to time. Only one client sends query, thats means database is not busy.

Where looking for problem? I dont uderstand what to do. Help me, please.

P.S. Sorry for my dreadful English, my native language is PHP ).

How many rows does this table have?

You have a quite a few indexes which will slow down updates.

Also note that KEY oenumsearch (oenumsearch) is a redundent index. Key lookups on the column oenumsearch can happily be performed on the KEY oenums (oenumsearch,tmid) index.

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Also note that KEY `oenumsearch` (`oenumsearch`) is a redundent index. Key lookups on the column oenumsearch can happily be performed on the KEY `oenums` (`oenumsearch`,`tmid`) index.
Thanks. I will drop this index. I knew this, but I did this for sure.
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How many rows does this table have?
About 7 000 000 and still growing. It will stop about 20 000 000 rows.
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You have a quite a few indexes which will slow down updates
I understand, that indexes is slow down updates. I dont understand, why one update fast, another update - slow?