Hello every one,
Maybe i did not formulate my researche right, but I just cant find the size of the FIFO buffer on a Arduino UNO AND also on a NANO.
Does any one know?
Ok never mind I found it. 
The fact that the UART in ATmega328 uses only 2 pins means no hardware flow control based on RTS/CTS or DSR/DTR is available. The USART0 in ATmega48/88/168/328 has a 2-character FIFO receive buffer and a Receive Shift Register, effectively providing a 3-char FIFO buffer.
Your Arduino sketch, the software running on Arduino board, can use Arduino Serial to talk with a computer. By checking the source code directory, it is easy to find that the Serial object is an instance of class HardwareSerial, see Arduino\arduino-0022\hardware\arduino\cores\arduino\HardwareSerial.h/cpp. Briefly browsing the implementation code shows that HardwareSerial is based on interrupt handling of serial hardware, with a ring buffer of either 32 or 128 characters (depending on hardware). It is a pretty simple class, and does not support XON/XOFF software flow control.
http://binglongx.wordpress.com/2011/10/26/arduino-serial-port-communication/