The sample of nearby LIRGs and ULIRGs for which dense molecular gas tracers have been measured is building up, allowing for the study of the physical and chemical properties of the gas in the variety of objects in which the most intense star formation and/or AGN activity in the local universe is taking place. This characterisation is essential to understand the processes involved, discard others and help to interpret the powerful starbursts and AGNs at high redshift that are currently being discovered and that will routinely be mapped by ALMA. We have studied the properties of the dense molecular gas in a sample of 17 nearby LIRGs and ULIRGs through millimeter observations of several molecules (HCO+, HCN, CN, HNC and CS) that trace different physical and chemical conditions of the dense gas in these extreme objects. In this paper we present the results of our HCO+ and HCN observations. We conclude that the very large range of measured line luminosity ratios for these two molecules severely questions the use of a unique molecular tracer to derive the dense gas mass in these galaxies.