Combinability of species in intercrops depends on the production conditions and there is limited information on the potential of intercropping under conventional (i.e., non-organic) management in Western Europe. Here we determined productivity of four crop species (maize, Zea mays L.; wheat, Triticum aestivum L.; faba bean, Vicia faba L.; pea, Pisum sativum L.) in six different bi-specific mixture compositions. Species were spring-sown and fertilized in their strips according to common practice for monocrops. Strips were 1.5 m wide enabling strong interspecific interactions. Intercrops with maize, a species sown and harvested later than the other three species, had land equivalent ratio (LER) values that were in four out of six cases significantly greater than one, from 1.14 ± 0.04 to 1.22 ± 0.05 in 2018, and from 0.98 ± 0.06 to 1.15 ± 0.01 in 2019. Simultaneous intercrops comprising two of the other three species had LER values that tended to be lower than one, even though many LERs were not significantly different from one: from 0.94 ± 0.02 to 0.95 ± 0.04 in 2018, and from 0.80 ± 0.08 to 0.93 ± 0.04 in 2019. The yield gain (net intercropping effect; NE) in relay intercrops with maize ranged from 1.33 ± 0.59 to 2.01 ± 0.54 Mg ha−1 in 2018, and from 0.29 ± 0.41 to 1.04 ± 0.14 Mg ha−1 in 2019. The NE of simultaneous intercrops ranged from −0.43 ± 0.13 to −0.27 ± 0.22 Mg ha−1 in 2018, and from −1.17 ± 0.49 to −0.36 ± 0.22 Mg ha−1 in 2019. Results indicate that temporal complementarity between species drove the LER (or NE) in these experiments. On the other hand, values of the LER (or NE) were similar in species combinations with or without legumes, suggesting no major role for complementarity for nitrogen capture under the conditions of the study. Faba bean was the most competitive species and reached high partial LER and NE values in intercrops at the expense of the companion species. Competition from faba bean reduced the grain yield of wheat and pea more than it increased faba bean grain yield, resulting in ...