A high-strength hot-rolled coated steel sheet having a constituent composition comprising, in a mass percent: C: 0.03% to 0.15%; Si: 0.4% or less; Mn: 1.2% to 1.9%; Ti: 0.05% to 0.25%; B: 0.0005% to 0.0050%; P: 0.03% or less; S: 0.005% or less; Al: 0.005% to 0.4%; N: 0.01% or less, optionally comprising one or more of Nb, V, Zr, Mo, Cr, W, Ta, and Hf in a total amount of 0.1% or less, and optionally one or more of: Ca: 0.005% or less; Mg: 0.005% or less; and REM: 0.005% or less in a total amount satisfying inequality: 0.5 ≤ % X * / 1.25 % S ≤ 5.0 where % X * = % X − 0.18 + 130 % X × % O, % X = % Ca + % Mg + % REM, and % O ≤ 0.005 %; and [%S], [%O], [%Ca], [%Mg], and [%REM] are contents, in a mass percent, of the individual elements and are zero if the elements are not present, the balance being Fe and incidental impurities, wherein the total amount of the incidental impurities Cu, Ni, Sb, As, Sn, and Pb is 1% or less, wherein a total area fraction of one or more of ferrite and tempered bainite is 90% or more, the steel sheet has a structure in which a volume fraction of Ti carbides having particle sizes of 20 nm or less is 0.05 vol% or more, wherein the volume fraction of Ti carbides having particle sizes of 20 nm or less is measured with the method disclosed in the description, the remaining structure consists of bainite, pearlite, martensite and/or retained austenite and the steel sheet has a coated layer or an alloyed coated layer on a surface thereof. C: 0.03% to 0.15%; Si: 0.4% or less; Mn: 1.2% to 1.9%; Ti: 0.05% to 0.25%; B: 0.0005% to 0.0050%; P: 0.03% or less; S: 0.005% or less; Al: 0.005% to 0.4%; N: 0.01% or less, optionally comprising one or more of Nb, V, Zr, Mo, Cr, W, Ta, and Hf in a total amount of 0.1% or less, and optionally one or more of: Ca: 0.005% or less; Mg: 0.005% or less; and REM: 0.005% or less in a total amount satisfying inequality: 0.5 ≤ % X * / 1.25 % S ≤ 5.0 where % X * = % X − 0.18 + 130 % X × % O, % X = % Ca + % Mg + % REM, and % O ≤ 0.005 %; and [%S], [%O], [%Ca], [%Mg], and [%REM] are contents, in a mass percent, of the individual elements and are zero if the elements are not present, the balance being Fe and incidental impurities, wherein the total amount of the incidental impurities Cu, Ni, Sb, As, Sn, and Pb is 1% or less, wherein a total area fraction of one or more of ferrite and tempered bainite is 90% or more, the steel sheet has a structure in which a volume fraction of Ti carbides having particle sizes of 20 nm or less is 0.05 vol% or more, wherein the volume fraction of Ti carbides having particle sizes of 20 nm or less is measured with the method disclosed in the description, the remaining structure consists of bainite, pearlite, martensite and/or retained austenite and the steel sheet has a coated layer or an alloyed coated layer on a surface thereof. Ca: 0.005% or less; Mg: 0.005% or less; and REM: 0.005% or less in a total amount satisfying inequality: 0.5 ≤ % X * / 1.25 % S ≤ 5.0 where % X * = % X − 0.18 + 130 % X × % O, % X = % Ca + % Mg + % REM, and % O ≤ 0.005 %; and [%S], [%O], [%Ca], [%Mg], and [%REM] are contents, in a mass percent, of the individual elements and are zero if the elements are not present, the balance being Fe and incidental impurities, wherein the total amount of the incidental impurities Cu, Ni, Sb, As, Sn, and Pb is 1% or less, wherein a total area fraction of one or more of ferrite and tempered bainite is 90% or more, the steel sheet has a structure in which a volume fraction of Ti carbides having particle sizes of 20 nm or less is 0.05 vol% or more, wherein the volume fraction of Ti carbides having particle sizes of 20 nm or less is measured with the method disclosed in the description, the remaining structure consists of bainite, pearlite, martensite and/or retained austenite and the steel sheet has a coated layer or an alloyed coated layer on a surface thereof.