The Corn Exchange at Wallingford seems to be something of a model for what a town amateur theatre should be. Standing on the spacious Market Square, built in 1856 of local stone in a restrained Victorian-Italianate style and housed in what was once the town Corn Exchange - an indoor market - it boasts a cheerful bar and a friendly welcome. The actual theatre space retains the massive cast iron spans supporting the roof, and the pink colour scheme – walls and seating – looks good under evening lighting.

Tom Stoppard's drama is more than half a century old now, but it's aged never a jot. It's located nominally in the closing years of Elizabeth I's reign as an offshoot of Hamlet, but it actually owes its being to the absurdist theatrical tradition of the mid- and late-fifties; to plays like Beckett's Waiting for Godot and Eugene Ionesco's Rhinocéros. Like them it occupies a non-specific place and a timeless era as it grapples with the fundamental mystery of the world about us. Stoppard has his two protagonists, bit-part players in Hamlet, spending their closing days in a state of confusion; unsure even of their own identities, they answer with equal readiness to their own and the other's name. They suffer from memory failure acute enough to conceal from them where they are headed, both literally and figuratively vis à vis the purpose of their summons to the Elsinore court.

The opening scene, in which director Lucy Pitman-Wallace, boasting a formidable C.V. in professional theatre, bathes her perfectly bare stage in a slightly queasy, greenish light has our two friends exploring the randomness of the universe as they endlessly toss coins which inexorably come up heads; this phenomenon is greeted by the duo with resignation punctuated by outbursts of frustration against their lack of free will.

The play's success rests and falls on the performances of the two lead actors, and it's wonderfully well-served by Will Lidbitter as Rosencrantz (or is it G...?) and Tom Richards as Guildenstern (or is it R...?), not least in their facility with the sheer length of their parts (they're on stage throughout the c. 2 hrs 20 mins playing time, excl. interval, and must have 80% of the dialogue).

Both are Everymen, but while Rosencrantz, in pantaloons and denim jacket, is a pragmatist, if not outright optimist, Stoppard cleverly shows development in his character, particularly his unexpected musings on life – or death - in a coffin. Guildenstern, a burly, bearded figure, is a questioner and a thinker, if an ineffectual one, and though on occasion with anxious pessimism he berates his friend, he also demonstrates humanity by offering him consolation on their doomed journey by ship to England. Both actors, in collaboration with their director, through movement and voice modulation, admirably find variety in their endless debates and joshing, along with plenty of humour that's now dry and now farcical, so that I had a constant sense of a rapt rather than a restless audience around me.

The remainder of the characters had their being in the scenes linking our heroes to their original existence as bit-players in Hamlet. Of these The Player, leader of the itinerant Tragedians, is a commanding but enigmatic figure ('we're actors – the opposite of people!'); both as a disreputable seller of sexual favours by his company of six ('We can do in flagrante delicto; that's realism!'), and seemingly the possessor of insights into the ultimate purpose of the events on stage. I enjoyed John Jones' mellifluous, ringing voice, but he might perhaps have seized the opportunity for a bit more outrageous eccentricity of manner and action.

Of his commedia dell'arte-style troupe, Teri Stevens was a sinister poisoner of Hamlet's father and Joel Webster, filling in at the last minute as the gender-ambiguous Alfred, played the part as though born to it. James Winter's Hamlet, a distracted figure with hair standing on end, was an appropriately moody presence. The playing of King Claudius, Queen Gertrude and Polonius was, however, a trifle colourless – they should improve as the run goes on.

Pitman-Wallace was admirably backed-up by the lighting design of John Evans and assistants, with a harsh light for our protagonists and a warm one for the court, and there was an atmospheric moment when the players clamber out of their ship barrels under a single, shuttered light. The ship set by Ian Knight and assistants of a sail poised high above piled up tubs and huge barrels on deck was a delight, and the elaborate costumes by Sue Forward and helpers cleverly anchored the production both in Shakespeare's theatre and yet timelessly out of it.

This was a first-class show from the Sinodun Players, demonstrating that Oxford has no local monopoly on drama that's challenging and yet entertaining.