An engine system is provided, including a controller which estimates a mass ratio (G/F) of intake air inside a cylinder (containing fresh air and burnt gas) to fuel, and controls devices of an engine at a given engine speed so that, while a demanded engine load is a first load, at least part of a mixture gas inside the cylinder combusts by flame-propagation when the estimated G/F is below a first G/F, and the entire mixture gas combusts by compression ignition when the estimated G/F is above the first G/F, whereas while the demanded load is a second load (> the first load), at least part of the mixture gas combusts by flame-propagation when the estimated G/F is below a second G/F (