The strike was announced as part of RMT's ongoing dispute with SWR over the future of guards and the introduction of driver-only operated trains.
In a letter to passengers on their website, managing director of SWR, Andy Mellors, wrote: "It is with great regret that I am writing to let you know that the RMT Executive has announced its intention to hold strikes on the South Western Railway, on 8 and 9 November.
"This is hugely disappointing given the positive talks we have been having with local union representatives.
"Our discussions have been around the introduction of a new fleet of suburban trains, which will start to arrive in 2019 and be fully introduced by December 2020."
He added: "These new trains can be operated in a variety of ways and we have been talking to the RMT about which method of operation will be most beneficial in terms of performance and customer service.
"As part of these discussions we have guaranteed that we will roster a guard on every train; and that those guards will continue to be trained in safety procedures."
There are also reduced services on the lines from Windsor & Eton Riverside to London Waterloo and Reading to London Waterloo which is affecting a number of stations including Whitton , Isleworth , Kew Bridge, Chiswick and Twickenham .
The RMT announced the planned strike action on October 24, with RMT general secretary Mick Cash saying: "The RMT remains deeply concerned SWR are prepared to cut corners on safety in order to run trains with staff who are ill-equipped to carry out the full range of functions of the guard.
"Instead of resorting to these desperate and risky measures, SWR should be round the table with the RMT working out a solution to this dispute which underpins the guarantee of a guard on their trains."
Those affected by the disruption have shared their thoughts on Twitter:
The strike runs alongside further walk-outs on Southern and Greater Anglia services.
To check live train time, head to South Western Railway's website .
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