The TARDIS lands at a space museum on the planet Xeros. The four companions set out to explore, but quickly realise that something is very odd: they leave no tracks, they can't touch anything, and nobody in the museum reacts to their presence. When they find themselves displayed as exhibits, the Doctor realises that they have jumped a time track, and are glimpsing their own future. When time catches up with them, they have no choice but to ally themselves with the native Xerons against the warlike Moroks who rule the planet, if they're to have any hope of averting their horrible destiny.

In 1964, Doctor Who story editor David Whitaker and South African writer Glyn Jones met at a dinner party, where they discussed a play of Jones' that Whitaker had recently enjoyed. Around the start of October, Whitaker suggested that Jones consider contributing to Doctor Who. At the time, Dennis Spooner was in the process of taking over as story editor, and so it was he who commissioned Jones to write The Space Museum. Jones was instructed to omit the Doctor from the third episode, so that William Hartnell could take a week's vacation.

In developing his ideas, Jones called his villains Moroks as a play on “moronic”, with Lobos' name suggested by the word “lobotomy”. The Xerons were originally called Tharls, drawing on an archaic term for a slave or servant from which the modern “thrall” was derived. The cause of the time distortion was originally a machine in the Morok processing room, rather than an issue with a TARDIS component. After Jones submitted his scripts, he was dismayed to learn that Spooner had excised much of the humorous content. Although Spooner generally enjoyed incorporating comedy into Doctor Who, he believed that jokiness would detract from the high-concept premise of The Space Museum. He also wanted to make sure that the season was made up of very distinct narratives.

Mervyn Pinfield's cost-saving efforts on The Space Museum included a minimal filming schedule

The director assigned to The Space Museum was Mervyn Pinfield who, a few months earlier, had concluded his appointment as Doctor Who's associate producer. During his tenure, Pinfield had also directed some episodes, most recently the majority of Planet Of Giants. Pinfield was aware that Spooner and producer Verity Lambert hoped to save money on The Space Museum, to compensate for the strain that The Web Planet had recently placed on the programme's resources, and in anticipation of the expense of the next serial in production, The Chase. Pinfield's cost-saving efforts included a minimal filming schedule at the BBC Television Film Studios in Ealing, London. This encompassed just a single day -- March 11th, 1965 -- and chiefly dealt with model shots.

As The Space Museum was being prepared for recording in April, a sea change was taking place in the Doctor Who production office. Lambert had already declared her intention to leave the show at the conclusion of the second recording block. Around the start of April, John Wiles was appointed as her successor. At about the same time, Spooner determined that he would not return to Doctor Who following the expiry of his six-month contract, in favour of working with Dalek creator Terry Nation on the high-profile adventure series The Baron. Doctor Who's third story editor would therefore be Donald Tosh. With the changeover in production team, Jacqueline Hill concluded that she would depart Doctor Who in The Chase along with William Russell, who had voiced the same decision some weeks earlier. The two stars' imminent exit was announced to the press on April 1st.

Production on The Space Museum was originally planned to begin on April 9th, skipping April 2nd, which was Good Friday. In the event, the first episode did, in fact, go before the cameras on the 2nd; the subsequent installments followed on consecutive Fridays. Unusually, The Space Museum was recorded in Studio 4 at BBC Television Centre in White City, London, rather than Doctor Who's usual home of Riverside Studio 1. Amongst the limited guest cast was Peter Craze, playing Dako; a year later, Craze's brother, Michael, would be cast as companion Ben Jackson. On April 16th, Hartnell was absent from the recording of The Search while enjoying his holiday.

The middle installments of The Space Museum both aired outside of Doctor Who's usual 5.40pm timeslot. On May 1st, episode two was scheduled fifteen minutes later to accommodate an extended edition of Grandstand, which was highlighted by the FA Cup Final between Leeds United and Liverpool. The following week, The Search was pushed to 6.00pm by a celebration of the twentieth anniversary of VE Day; this special broadcast also preempted Doctor Who's usual lead-in, Juke Box Jury.

• Doctor Who Magazine #316, 1st May 2002, “Archive: The Space Museum” by Andrew Pixley, Panini Publishing Ltd.
• Doctor Who Magazine Special Edition #7, 12th May 2004, “I'm Into Something Good” by Andrew Pixley, Panini Publishing Ltd.
• Doctor Who: The Complete History #5, 2016, “Story 15: The Space Museum”, edited by John Ainsworth, Hachette Partworks Ltd.
• Doctor Who: The Handbook: The First Doctor by David J Howe, Mark Stammers and Stephen James Walker (1994), Virgin Publishing.
• Doctor Who: The Sixties by David J Howe, Mark Stammers and Stephen James Walker (1992), Virgin Publishing.