Context : The Kepler K2 mission now makes it possible to find and study a wider variety of eclipsing binary stars than has been possible to-date , particularly long-period systems with narrow eclipses .

Aims : Our aim is to characterise eclipsing binary stars observed by the Kepler K2 mission with orbital periods longer than P \approx 5.5 days .

Methods : The ellc binary star model has been used to determine the geometry of eclipsing binary systems in Kepler K2 campaigns 1 , 2 and 3 .
The nature of the stars in each binary is estimated by comparison to stellar evolution tracks in the effective temperature – mean stellar density plane .

Results:43 eclipsing binary systems have been identified and 40 of these are characterised in some detail .
The majority of these systems are found to be late-type dwarf and sub-giant stars with masses in the range 0.6 – 1.4 solar masses .
We identify two eclipsing binaries containing red giant stars , including one bright system with total eclipses that is ideal for detailed follow-up observations .
The bright B3V-type star HD 142883 is found to be an eclipsing binary in a triple star system .
We observe a series of frequencies at large multiples of the orbital frequency in BW Aqr that we tentatively identify as tidally induced pulsations in this well-studied eccentric binary system .
We find that the faint eclipsing binary EPIC 201160323 shows rapid apsidal motion .
Rotational modulation signals are observed in 13 eclipsing systems , the majority of which are found to rotate non-synchronously with their orbits .

Conclusions : The K2 mission is a rich source of data that can be used to find long period eclipsing binary stars .
These data combined with follow-up observations can be used to precisely measure the masses and radii of stars for which such fundamental data are currently lacking , e.g. , sub-giant stars and slowly-rotating low-mass stars .