An engine controlling apparatus for executing, during running of a vehicle, at least one of (i) an engine automatic stop control for automatically stopping an engine of the vehicle and (ii) an engine automatic restart control for automatically restarting the engine, said engine controlling apparatus comprising: an allowing/inhibiting device configured to selectively allow and inhibit execution of the least one of (i) the engine automatic stop control and (ii) the engine automatic restart control, by comparing (a) a plurality of physical amounts (|dθ|, |γ|, |β|, |αf|, |Δγ|, |θ|, |G|, μ) including (a-1) behavior-representing physical amounts (|dθ|, |γ|, |β|, |αf|, |Δγ|, |θ|, |G|) each representing behavior of the vehicle and (a-2) a friction coefficient (μ) of a road surface, with (b) a threshold value (dθth, γth 1, γth 2, Gxth, βth, μth) which is determined, depending on a running velocity (v) of the vehicle, for said each of the at least one of the physical amounts, wherein the behavior-representing physical amounts include at least one turning-behavior-representing physical amount (|dθ|, |γ|, |β|, |αf|, |Δγ|, |θ|) representing the behavior of the vehicle upon turning of the vehicle, wherein said allowing/inhibiting device includes a turning-behavior-basis allowing/inhibiting portion that is configured to inhibit the execution of the engine automatic restart control, when each of the at least one turning-behavior-representing physical amount (|dθ|, |γ|, |β|, |αf|, |Δγ|, |θ|) is larger than the threshold value (dθth, γth 1, γth 2, βth) which is determined for said each of the at least one turning-behavior-representing physical amount, and wherein said turning-behavior-basis allowing/inhibiting portion of said allowing/inhibiting device includes a running-velocity-basis threshold-value determiner (10, S3; S33) that is configured to determine the threshold value (dθth, γth 1, γth 2, βth, μth) such that the determined threshold value is smaller when the running velocity (v) of the vehicle is high than when the running velocity of the vehicle is low. an allowing/inhibiting device configured to selectively allow and inhibit execution of the least one of (i) the engine automatic stop control and (ii) the engine automatic restart control, by comparing (a) a plurality of physical amounts (|dθ|, |γ|, |β|, |αf|, |Δγ|, |θ|, |G|, μ) including (a-1) behavior-representing physical amounts (|dθ|, |γ|, |β|, |αf|, |Δγ|, |θ|, |G|) each representing behavior of the vehicle and (a-2) a friction coefficient (μ) of a road surface, with (b) a threshold value (dθth, γth 1, γth 2, Gxth, βth, μth) which is determined, depending on a running velocity (v) of the vehicle, for said each of the at least one of the physical amounts, wherein the behavior-representing physical amounts include at least one turning-behavior-representing physical amount (|dθ|, |γ|, |β|, |αf|, |Δγ|, |θ|) representing the behavior of the vehicle upon turning of the vehicle, wherein said allowing/inhibiting device includes a turning-behavior-basis allowing/inhibiting portion that is configured to inhibit the execution of the engine automatic restart control, when each of the at least one turning-behavior-representing physical amount (|dθ|, |γ|, |β|, |αf|, |Δγ|, |θ|) is larger than the threshold value (dθth, γth 1, γth 2, βth) which is determined for said each of the at least one turning-behavior-representing physical amount, and wherein said turning-behavior-basis allowing/inhibiting portion of said allowing/inhibiting device includes a running-velocity-basis threshold-value determiner (10, S3; S33) that is configured to determine the threshold value (dθth, γth 1, γth 2, βth, μth) such that the determined threshold value is smaller when the running velocity (v) of the vehicle is high than when the running velocity of the vehicle is low.