Fibroblast growth factor receptors (FGFRs) can act as driving oncoproteins in certain cancers, making them attractive drug targets. Here we have characterized tumour cell responses to two new inhibitors of FGFR1-3, AZ12908010 and the clinical candidate AZD4547, making comparisons with the well-characterized FGFR inhibitor PD173074. In a panel of 16 human tumour cell lines, the anti-proliferative activity of AZ12908010 or AZD4547 was strongly linked to the presence of deregulated FGFR signalling, indicating that addiction to deregulated FGFRs provides a therapeutic opportunity for selective intervention. Acquired resistance to targeted tyrosine kinase inhibitors is a growing problem in the clinic but has not yet been explored for FGFR inhibitors. To assess how FGFR-dependent tumour cells adapt to long-term FGFR inhibition, we generated a derivative of the KMS-11 myeloma cell line (FGFR(Y373C)) with acquired resistance to AZ12908010 (KMS-11R cells). Basal phosphorylated FGFR and FGFR-dependent downstream signalling were constitutively elevated and refractory to drug in KMS-11R cells. Sequencing of FGFR3 in KMS-11R cells revealed the presence of a heterozygous mutation at the gatekeeper residue, encoding FGFR3(V555M); consistent with this, KMS-11R cells were cross-resistant to AZD4547 and PD173074. These results define the selectivity and efficacy of two new FGFR inhibitors and identify a secondary gatekeeper mutation as a mechanism of acquired resistance to FGFR inhibitors that should be anticipated as clinical evaluation proceeds.