Branched polypropylenes (PPb) with markedly improved melt strength were produced without significantly affecting the processability of the original PP. A two‐step process of functionalization with MA and crosslinking with m‐XDA was used, both by batch mixing and by extrusion. Branching degrees of ~0.06 LCB/1000 monomer units or smaller were obtained. All PPbs display clear and significant strain hardening, being the PPb obtained by extrusion the one that shows the largest melt strength. This polymer has a zero‐shear‐rate viscosity slightly smaller than that of PP while its strain‐hardening index is about 10 times higher. Moreover, the nonlinear behavior of PP at elongation begins at a time similar to its terminal relaxation time or larger, while the ratio of these times reduces significantly with branching. PP/PPb blends were prepared to extend the range of obtainable melt strength in PP. They display rheological behavior between those of the mixed polymers with slight positive deviation. © 2019 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019, 137, 48845.