OK guies.
I missed some replies and I must study them before you give more information.
Many thanks to all.
I've been doing so many mistake and so giving so many wrong information in my previous post.
Hopefully you made me figuring them out but I hope it won't confuse other beginners.
In fact, I 'm using a 2kb and a 4kb Eeprom and the 4kb must be seen as 2 devices (thanks to Nicks' I2C scanner) and it needs the pull up resistor despite the Arduino has small 40kohm ones (too weak for more capacitive circuit, like long line or more than one Eeprom....I'm learning...