The purpose of this paper is to investigate the volatility spillovers between the returns on crude oil futures and oil company stocks using alternative multivariate GARCH models, namely the CCC model of Bollerslev (1990), VARMA-GARCH model of Ling and McAleer (2003), and VARMA-AGARCH model of McAleer et al. (2008). The paper investigates WTI crude oil futures returns and the stock returns of ten oil companies, which comprise the "supermajor" group of oil companies, namely Exxon Mobil (XOM), Royal Dutch Shell (RDS), Chevron Corporation (CVX), ConocoPhillips (COP), BP (BP) and Total S.A. (TOT), and four other large oil and gas companies, namely Petrobras (PBRA), Lukoil (LKOH), Surgutneftegas (SNGS), and Eni S.p.A. (ENI). Estimates of the conditional correlations between the WTI crude oil futures returns and oil company stock returns are found to be quite low using the CCC model, while the VARMA-GARCH and VARMA-AGARCH models suggest no significant volatility spillover effects in any pairs of returns. The paper also presents evidence of the asymmetric effects of negative and positive shocks of equal magnitude on the conditional variances in all pairs of returns.