We report optical observations of the GRB 980329 error box which represent the second earliest detection of the GRB 980329 optical transient. We determine R = 23.7 +/- 0.5 mag on 29.89 March, which is consistent with R = 23.6 +/- 0.2 mag as reported by Palazzi et al. (1998) on 29.99 March. Based on extrapolations of the light curve we claim that the R-band magnitude of the GRB 980329 host galaxy should lie in the range 26.8 mag < R < 29 mag. We also discuss the similarities with GRB 970111. Based on observations carried out at the 1.0-m Jacobus Kapteyn Telescope operated by the Royal Greenwich Observatory in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias. Based on observations carried out at the 1.5-m Telescope of the Observatorio Astronomico Nacional in Calar Alto. Based on observations carried out at the 1.0-m Optical Ground Station telescope of the European Space Agency in the Spanish Observatorio del Teide of the Instituto de Astrofisica de Canarias.