A Retinoic Acid Receptor antagonist or a RAR inverse agonist which binds to receptors of the RARα, RARβ and RARγ subtypes, for use in the treatment of chemotherapy and/or radiation therapy side effects in a mammal undergoing chemotherapy and/or radiation therapy, wherein the side effects is neutropenia, leucopenia or thrombocytopenia, wherein the RAR antagonist or RAR inverse agonist has the chemical structure according to Formula: or a pharmaceutically acceptable salt thereof; wherein X is S, O, NR where R is H or alkyl of 1 to 6 carbons, or X is [C(R 1) 2] n where R 1 is independently H or an alkyl of 1 to 6 carbons, and n is an integer between, and including, 0 and 2; R 2 independently are hydrogen, an alkyl of 1 to 6 carbons, F, Cl, Br, I, CF 3, fluoro substituted alkyl of 1 to 6 carbons, OH, SH, alkoxy of 1 to 6 carbons, or alkylthio of 1 to 6 carbons; R 3 independently are hydrogen, alkyl of 1 to 6 carbons or F; m is an integer having the value of 0-3; n is an integer having the value of 0-4; o is an integer having the value of 0-3; Z is -CONR 1 -, -CSNR 1 -, -NR 1 CO-, -NR 1 CS-, -C≡C-, -C=C-, -N=N-, -N=CR 1 -, -CR 1 =N-,-COO-, -OCO-; -OSO-; -OCS-, or -(CR 1 =CR 1) n' - where n' is an integer from 0 to 5; Y is a phenyl or naphthyl group, or a heteroaryl selected from a group consisting of pyridyl, thienyl, furyl, pyridazinyl, pyrimidinyl, pyrazinyl, thiazolyl, oxazolyl, imidazolyl and pyrrazolyl, the phenyl and heteroaryl groups being optionally substituted with one or two R 2 groups, or when Z is -(CR 1 =CR 1) n' - and n' is 3, 4 or 5 then Y represents a direct valence bond between said (CR 2 =CR 2) n' group and B; A is (CH 2) q where q is 0-5, a branched chain alkyl having 3 to 6 carbons, cycloalkyl having 3 to 6 carbons, alkenyl having 2 to 6 carbons and 1 or 2 double bonds, alkynyl having 2-6 carbons and 1 or 2 triple bonds; B is hydrogen, COOH or a pharmaceutically acceptable salt thereof, COOR 8, CONR 9 R 10, CH 2 OH, CH 2 OR 11, CH 2 OCOR 11, CHO, CH(OR 12) 2, CHOR 13 O, -COR 7, CR 7 (OR 12) 2, CR 7 OR 13 O, or a tri-alkylsilyl where the alkyl groups have 1 to 6 carbons; R 7 is an alkyl, cycloalkyl or alkenyl group containing 1 to 5 carbons; R 8 is an alkyl group of 1 to 10 carbons or trimethylsilylalkyl where the alkyl group has 1 to 10 carbons, a cycloalkyl group of 3 to 10 carbons, phenyl or a lower alkylphenyl where the alkyl group has 1 to 6 carbons; R 9 and R 10 independently are hydrogen, an alkyl group of 1 to 10 carbons, a cycloalkyl group of 3 to 10 carbons, phenyl or a lower alkylphenyl where the alkyl group has 1 to 6 carbons; R 11 is an alkyl of 1 to 6 carbons, phenyl or alkylphenyl where the alkyl group has 1 to 6 carbons; R 12 is an alkyl of 1 to 6 carbons; R 13 is a divalent alkyl radical of 2 to 5 carbons; R 14 is (R 15) r -phenyl, (R 15) r -naphthyl, or (R 15) r -heteroaryl wherein the heteroaryl group has 1 to 3 heteroatoms selected from the group consisting of O, S and N, and r is an integer having the values of 0-5; and R 15 is independently H, F, Cl, Br, I, NO 2, N(R 8) 2, N(R 8)COR 8, NR 8 CON(R 8) 2, OH, OCOR 8, OR 8, CN, an alkyl group having 1 to 10 carbons, a fluoro substituted alkyl group having 1 to 10 carbons, an alkenyl group having 2 to 10 carbons and 1 to 3 double bonds, an alkynyl group having 2 to 10 carbons and 1 to 3 triple bonds, or a trialkylsilyl or trialkylsilyloxy group where the alkyl groups independently have 1 to 6 carbons.