Locking multiple objectsat same time?

Hi All,
I have a design question for an LRU cache class. The class has a hashmap which acts as the cache and a linked list with the most recently accessed item at the head of the list. Both of them together help to maintain an LRU cache.
Now when I need to perform operations like add, update, remove items from the LRU cache, I need to add, update, delete from the cache as well as the linked list. So all my methods need to ensure thread-safe concurrency on 2 shared objects (hashmap and linked list) at same time, and not only on one shared object. How can I achieve this?
I do not plan to synchronize the methods, but I plan to synchronize on the shared objects. In method 1 if I synchronize on the hashmap, then any other thread can enter method 2 and can modify the linked list. If I I synchronize on linked list, then same problem will be there for hashmap. So how can I synchronize on both the objects at same time??
or should I synchronize on the 'this' object (object of LRU cache) itself? ( I do not want to do this)
or should i declare the methods to be synchronized? ( i do not want to do this)
Any comments will be highly appreciated.
Thanks.

Why do i feel that it is not possible...
So it means that if I have
LRUCache obj = new LRUCache();
then,
synchronized(obj){ /// }
and
synchronized(obj.obj1) {//}
are both possible by 2 different threads?
I know that obj and obj.obj1 are 2 different objects, but one is a part of another, isn't it? So it should not be possible?

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If there is someone who would like to look at this problem I'd like to show you program log files with verbose output turned on. There are 11 log files in the archive: http://bin.mypage.sk/FILES/log.rar
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4000|0 4 20100922 07:07:24.094 20100922 07:07:24.094 FLOW_CMD
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fileops: close db_files/__db.001
fileops: open db_files/__db.001
fileops: mmap db_files/__db.001
fileops: close db_files/__db.001
unable to join the environment
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fileops: unlink db_files/__db.004
fileops: unlink db_files/__db.003
fileops: unlink db_files/__db.002
fileops: unlink db_files/__db.001
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fileops: mmap db_files/__db.005
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fileops: read db_files/log.0000000001: 28 bytes
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Recovery starting from [1][243]
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fileops: open db_files/log.0000000002
fileops: close db_files/log.0000000002
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fileops: close db_files/log.00002
fileops: open db_files/log.0000000001
fileops: seek db_files/log.0000000001 to 463
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fileops: write db_files/log.0000000001: 4096 bytes
fileops: write db_files/log.0000000001: 4096 bytes
fileops: write db_files/log.0000000001: 4096 bytes
fileops: write db_files/log.0000000001: 3633 bytes
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Recovery complete at Wed Sep 22 07:07:23 2010
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db_create
dbp->open
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fileops: read db_files/log.0000000001: 28 bytes
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fileops: flush db_files/log.0000000001
fileops: open db_files/__db.80000001.d9f23b56
fileops: stat db_files/__db.80000001.d9f23b56
fileops: seek db_files/__db.80000001.d9f23b56 to 0
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fileops: seek db_files/__db.80000001.d9f23b56 to 4096
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fileops: flush db_files/__db.80000001.d9f23b56
fileops: close db_files/__db.80000001.d9f23b56
fileops: stat db_files/test_aaps.db
fileops: stat db_files/__db.80000001.d9f23b56
fileops: unlink db_files/__db.80000001.d9f23b56
fileops: open db_files/log.0000000001
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DB_TXN->abort: log undo failed for LSN: 1 463: Input/output error
fileops: close db_files/log.0000000001
PANIC: Input/output error
fileops: open db_files/log.0000000001
fileops: read db_files/log.0000000001: 12 bytes at offset 463
PANIC: fatal region error detected; run recovery
DB_LOGC->get: LSN: 1/463: read: DB_RUNRECOVERY: Fatal error, run database recovery
DB_TXN->abort: log undo failed for LSN: 1 463: DB_RUNRECOVERY: Fatal error, run database recovery
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PANIC: DB_RUNRECOVERY: Fatal error, run database recovery
PANIC: DB_RUNRECOVERY: Fatal error, run database recovery
dbp->open end
dbp->close
PANIC: fatal region error detected; run recovery
envp->close
File handles still open at environment close
Open file handle: db_files/log.0000000001
fileops: close db_files/log.0000000001
PANIC: fatal region error detected; run recovery
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