We prove the existence of local and global in time weak solutions for the equations of nonhomogeneous incompressible asymmetric fluids in a bounded domain Omega subset of R-3, when the initial vacuum is allowed, i.e., the initial density rho(0) is not necessarily strictly positive. Our solutions here are more regular than previous results and so satisfy the initial conditions in a stronger sense. The global in time solutions are obtained under smallness assumptions on the initial data and forcing terms. (C) 2019 Elsevier Inc. All rights reserved.