In this paper we provide evidence for the intermittent nature of the fluctuations of the flow velocity and Alfven velocity in the inner solar wind between 0.3 and 1.0 AU. We analyse the p-th order structure functions in the time domain between 40.5 seconds (instrumental resolution period) and 24 hours, and investigate their scaling properties in the Alvenic range from fractions of minutes to several hours. Generally, the fast and slow wind regimes have to be discriminated, because the scaling features of the velocity differences with time lag r vary systematically with the wind speed. Radial trends are established by comparison of Helios data obtained near 0.3 AU and 1.0 AU. The second-order structure function for p=2, which is equivalent to the power spectrum, shows essentially an exponent s(p)=α−1, as is predicted from self-similar scaling for a spectral index α. Yet there appears substantial departure from simple self-similarity, and also from homogeneous intermittency (uniform fractality) at higher-order p's for all types of flows analysed, which is clearly evident in the normalized dimensionless structure functions