Hi Jan,
Answer your two questions:
1. RXBRK problem in interrupt
When you enable the LIN break interrupt, do you also enable other interrupt?
Please check this register:


You can just enable the DELTARXBRKEN bit, don't enable other interrupt.
Then when the LIN break happens, you can check UART_STAT[DELTARXBRK] and UART_STAT[RXBRK].
Please check it at first, what I am afraid, when the first time you read the LIN1_USART->STAT, the interrupt is not caused by the LIN break. so, please check the interrupt enable register, make sure you just enable the LIN break interrupt at first.
2. what the LINMODE in CFG does?
This is the LIN break mode enable, the register already give the description.

If you use the LIN bus, you need to set this bit to enable the LIN bus break detect function. Otherwise, the UART is the normal UART break function, not the LIN break function.
About the difference between the normal break and the LIN break, please check these description:

When you enable the LINMODE, after RX input remains low for 11 bit times, you will get the break state,and the received data is not stored in teh receive data buffer, buf if you are using the normal operation, you will also receive the character, and the framing error status.
You can check it on your side.
If you still have question about this topic, please kindly let me know!
Have a great day,
Kerry
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