Frequency discrepancies in real-time SA

Hi all
I was just doing some setting up on some low frequency stuff and noticed an odd thing. Here goes:

BB60-c
Sno20181889
S/W 3.8.9

CF = 1 MHz
Span = 500 kHz
RBW = 10 kHz
Standard sweep.
Peak is central on graticule and ‘peak search identifies signal at 1.000976 MHz, which is OK.

Change to real time analysis and the peak moves to the right and the marker ‘falls off’ down the LF slope. Peak search finds the peak and says the frequency is 1.00577 MHz.
If I now change the RBW to 3 kHz, peak returns to centre and marker falls down HF slope.
Something a bit odd going on…
I can send screenshots if required.

Andy.