This paper deals with the Hybrid Cramer-Rao bound (HCRB) for the estimation of Rayleigh channel and carrier frequency offset (CFO) in data-aided (DA) and non-data-aided (NDA) OFDM systems. The random part (channel) and the deterministic part (CFO) of the hybrid vector to be estimated are statistically independent. The channel estimation function is based on the equivalent discrete-time channel taps or on the physical propagation channel parameters. This bound is derived in on-line and off-line scenarios for time-invariant and time-varying channel within one OFDM block, assuming the availability of prior information. In NDA context, whereas this true HCRB is hard to evaluate, we present a closed-form expression of a HCRB, i.e., the Modified HCRB (MHCRB). Our claims are supported by theoretical and simulation results, which are obtained considering Jakes' channels with high Doppler spread.