We test the behavioural theories of overconfidence and underreaction on cross-sectional (CS) and time-series (TS) momentum returns in the Japanese stock markets. Both CS and TS momentum returns are large and significant when the market continues in the same state and turns into losses when the market transitions to another state, consistent with the overconfidence but not the underreaction model. We find that TS conditional momentum returns exceed conditional CS momentum returns because of its active position since TS takes a net long (short) position following UP (DN) markets while CS is a zero-cost strategy irrespective of the market state. Finally, we find no relation between idiosyncratic volatility (IV) and momentum returns which is not supportive of either the overconfidence or underreaction model but implies that IV is not a significant limit to arbitrage in Japan.