We study a sample composed of 28 of the brightest stars in the Arches cluster. Our aim is to constrain their stellar and wind properties and to establish th eir nature and evolutionary status. We analyze K-band spectra obtained with the integral field spectrograph SINFONI on the VLT. Atmosphere models computed with the code CMFGEN are used to deri ve the effective temperatures, luminosities, stellar abundances, mass loss rates and wind terminal velocities. We find that the stars in our sample are either H-rich WN7-9 stars (WN7-9h) or supergiants, where two are classified as OIf+. All stars are 2-4 Myr old. There is marginal evidence for a younger age among the most massive stars. The WN7-9h stars reach luminosities as high as 2 * 106 L_o, con sistent with initial masses of 120 Msun. They are still quite H-rich, but show both N enhancement and C depletion. They are thus identified as core H-bu rning objects showing products of the CNO equilibrium on their surface. Their progenitors are most likely supergiants of spectral types earlier than O4-6 and i nitial masses > 60 Msun. Their winds follow a well-defined modified wind momentum - luminosity relation (WLR): this is a strong indication that they are rad iatively driven. Stellar abundances tend to favor a slightly super-solar metallicity, at least for the lightest metals. We note, however, that the evolutionary models seem to under-predict the degree of N enrichment.