Tickets will be accepted on South West Trains services, said Southern.
A spokesman for Southern GTR said the disruption was likely to last for the rest of the week.
This follows a RMT conductors’ strike on Tuesday last week. Talks between the union and company stalled on Friday.
Chief Operating Officer Dyan Crowther said: “We are extremely disappointed and frustrated that, due to an unusually high level of sickness among some of our conductors and some others not working their normal rest days, we are unable to run the full service between Southampton and Brighton.”
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Two other walk-outs have been planned in May.