HAL_UART_Receive_DMA(&huart1,... and HAL_UART_Receive_DMA(&huart2,.... Usually work well but not if I use in the same program TIM2 with the following instruction HAL_TIM_Base_Start_IT(&htim2).... The timer TIM2 keep working.

[Tesla DeLorean]

Please don't put the entire question in the title/summary.

Identify the model of STM32 and make/model of board you are working with.

I​s TIM2 interrupting at some excessively high rate? ie more than few hundred KHz

[S.Ma]

Inctease the stack size a bit, put all non systick interrupts at same level and check if tim and usart are sharing the same intweeupt vector, or that your code is stuck in interrupt. Debug witg stlink to nail down what is wrong.

[Karl Yamashita]

Paste your code so we can better see what could be the issue.