Abstract. We performed a deep infrared imaging survey of 63 embedded young stellar objects (YSOs) located in the Taurus and Ophiuchus clouds to search for companions. The sample includes Class I and flat infrared spectrum protostellar objects. We find 17 companions physically bound to 15 YSOs with angular separations in the range 0.8-10 (110-1400 AU) and derive a companion star fraction of 23 ± 9% and 29 ± 7% for embedded YSOs in Taurus and Ophiuchus, respectively, about twice as large as that found among G dwarfs in the solar neighborhood. Therefore, binary and multiple protostellar systems are a very frequent outcome of the fragmentation of prestellar cores. In spite of different properties of the clouds and especially of the prestellar cores, the fraction of wide companions, 27 ± 6% for the combined sample, is identical in the two star-forming regions. This suggests that the frequency and properties of wide multiple protostellar systems are not very sensitive to specific initial conditions. Comparing the companion star fraction of the youngest YSOs still surrounded by extended envelopes to that of more evolved YSOs, we find evidence for a possible evolution of the fraction of wide multiple systems, which seems to decrease by a factor of about two on a timescale of ∼10 5 yr. For the first time it is possible to confront the result of a multiplicity survey of a nearly complete population of embedded YSOs at an age of ∼10 5 yr to numerical simulations of molecular cloud collapse which, after a few free fall times, reach this evolutionary stage. Somewhat contrary to model predictions, we do not find evidence for a sub-clustering of embedded sources at this stage on a scale of a few 100 AU that could be related to the formation of small-N protostellar clusters. Possible interpretations of this discrepancy are discussed.