Preventing deadlock.

I have two tasks, both invoke the same proc in package mypkg.

The proc inserts into a table. Thus we have two sessions inserting into same table through a proc in mypkg.

Thus, Task1 and Task2 tasks failed due to deadlock issue,

Logs:
25-MAY-12 04.51.56.680350000 AM "[do_stuff]{}
Stack:
ORA-00060: deadlock detected while waiting for resource
Backtrace:
ORA-06512: at "DEV.mypkg", line 123"


25-MAY-12 04.51.44.221277000 AM "[do_stuff]{}
Stack:
ORA-00060: deadlock detected while waiting for resource
Backtrace:
ORA-06512: at "DEV.mypkg", line 123"


both tasks finished successfully on rerun induvidually.

What can i do to prevent such deadlock issues when two sessions call the same proc in a package.