micrOMEGAs is a code to compute dark matter observables in generic extensions of the standard model. This version of micrOMEGAs includes a generalization of the Boltzmann equations to take into account the possibility of two,dark matter candidates. The modification of the relic density calculation to include interactions between the two dark matter sectors as well as semi-annihilation is presented. Both dark matter signals in direct and indirect detection are computed as well. An extension of the standard model with two scalar doublets and a singlet is used as an example. Program summary Program title: MicrOMEGAs4.1 Catalogue identifier: ADQR_v4_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADQR_v4_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 738425 No. of bytes in distributed program, including test data, etc.: 9807620 Distribution format: tar.gz Programming language: C and Fortran. Computer: PC, Mac. Operating system: UNIX (Linux, Darwin). RAM: 50MB depending on the number of processes required. Classification: 1.9, 11.6. Catalogue identifier of previous version: ADQR_v3.0 Journal reference of previous version: Comput. Phys. Comm. 185 (2014) 960 External routines: CalcHEP, SuSpect, NMSSMTools, CPSuperH, LoopTools, HiggsBounds Does the new version supersede the previous version?: Yes Nature of problem: Calculation of the relic density and direct and indirect detection rates of the lightest stable particle in particle physics models with at most two stable dark matter candidates. Solution method: hi the case where the two dark matter particles have very different masses, we find that the equations for the evolution of the density of dark matter behave as stiff equations. To solve these we use the backward scheme and the Rosenbrock algorithm. The standard solution based on the Runge-Kutta method is still used for models with only one dark matter candidate. Reasons for new version: There are many experiments that are currently searching for the remnants of dark matter annihilation and the relic density is determined precisely from cosmological measurements. In this version we generalize the Boltzmann equations to take into account the possibility of two dark matter candidates. Thus, in solving for the relic density we include interactions between the two dark matter sectors as well as semi-annihilation. The dark matter signals in direct and indirect detection are computed as well. Summary of revisions: Generalization of the Boltzmann equations to include two dark matter candidates, their interactions and semi-annihilations, the relative density of the two dark matter components is taken into account when computing direct/indirect detection rates. Upgrade of the numerical method for solving the Boltzmann equations. Include sample extensions of the standard model with extra doublet and singlets which contain two stable neutral particles. Unusual features: Depending on the parameters of the model, the program generates additional new code, compiles it and loads it dynamically. Running time: 4 sec (C) 2015 Elsevier B.V. All rights reserved.