Using SysTick_Handler in mbed LPC1768 project
As said in the comments, the SysTick timer is indeed in use by the RTOS and you should not muck with this. Use the Ticker class if you need to tick regularly, it will drive the underlying high-precision timer on the platform (and is portable code). An additional benefit is that multiple Tickers can be created and they'll all use the same hardware timer.

void tick() {
    // do things, note that this runs in an ISR
}

Ticker t;
t.attach_us(&amp;tick, 1000 /* 1ms. */);