We present a quantitative estimate of the relative active galactic nucleus (AGN)/starburst content in a sample of 59 nearby (z < 0.15) infrared bright ultraluminous infrared galaxies (ULIRGs) taken from the 1‐Jy sample, based on infrared L‐band (3–4 μm) spectra. By using diagnostic diagrams and a simple deconvolution model, we show that at least 60 per cent of local ULIRGs contain an active nucleus, but the AGN contribution to the bolometric luminosity is relevant only in ∼15–20 per cent of the sources. Overall, ULIRGs appear to be powered by the starburst process, responsible for >85 per cent of the observed infrared luminosity. The subsample of sources optically classified as low‐ionization nuclear emission‐line regions (LINERs; 31 objects) shows a similar AGN/starburst distribution as the whole sample, indicating a composite nature for this class of objects. We also show that a few ULIRGs, optically classified as starbursts, have L‐band spectral features suggesting the presence of a buried AGN.