We study the leptoquark model of Buchmuller, Ruckl and Wyler, focusing on a particular type of scalar ($R_2$) and vector ($U_1$) leptoquark. The primary aim is to perform the calculations for leptoquark production and decay at next-to-leading order (NLO) to establish the importance of the NLO contributions and, in particular, to determine how effective the narrow-width-approximation (NWA) is at NLO. For both the scalar and vector leptoquarks it is found that the NLO contributions are large, with the larger corrections occurring for the case vector leptoquarks. For the scalar leptoquark it is found that the NWA provides a good approximation for determining the resonant peak, however the NWA is not as effective for the vector leptoquark. For both the scalar and vector leptoquarks there are large contributions away from the resonant peak, which are missing from the NWA results, and these make a significant difference to the total cross-section.
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