This study examines the dynamic relationship between monthly inflation and inflation uncertainty in Japan, the US and the UK by employing linear and nonlinear Granger causality tests for the 1957:01-2006:10 period. Using a generalised autoregressive conditional heteroskedasticity (GARCH) model to generate a measure of inflation uncertainty, the empirical evidence from the linear and nonlinear Granger causality tests indicate a bidirectional causality between the series. The estimates from both the linear vector autoregressive (VAR) and nonparametric regression models show that higher inflation rates lead to greater inflation uncertainty for all countries as predicted by Friedman (1977). Although VAR estimates imply no significant impact, except for Japan, nonparametric estimates show that inflation uncertainty raises average inflation in all countries, as suggested by Cukierman and Meltzer (1986). Thus, inflation and inflation uncertainty have a positive predictive content for each other, supporting the Friedman and Cukierman-Meltzer hypotheses, respectively.