A process for preparing a sample containing genetic material for in situ analysis of DNA or RNA or a surrogate thereof, the process comprising: a) contacting the sample containing genetic material with a lysis mixture under conditions and for a time to produce a lysate, wherein the lysis mixture comprises: proteinase K or an enzymatically active mutant or variant thereof, and a surfactant that substantially lacks fluorescence between 300 nm and 750 nm when in use for in situ analysis of DNA or RNA or a surrogate thereof, and wherein when in use for in situ analysis of RNA or a surrogate thereof the lysis mixture is substantially free of a cation chelator and additionally comprises a polypeptide having deoxyribonuclease activity, and b) admixing the lysate with a stop mixture at substantially the same temperature as the contacting step a) to form a stopped mixture, wherein the stop mixture comprises: at least one alkoxysuccinyl-peptidyl-haloalkyl ketone wherein the peptidyl portion of the ketone comprises SEQ ID NO:5, SEQ ID NO:7 or SEQ ID NO:9; wherein the halo of haloalkyl is mono- or di- chloro, bromo, or iodo and the alkyl of haloalkyl or alkoxy is C 1 -C 3 alkyl, wherein the peptidyl portion of the at least one alkoxysuccinyl-peptidyl-haloalkyl ketone is a tetrapeptide or a pentapeptide. and when in use for in situ analysis of RNA or a surrogate thereof additionally a cation chelator effective to inactivate the polypeptide having deoxyribonuclease activity, and wherein the stopped mixture is thereby prepared for in situ analysis of DNA or RNA or a surrogate thereof. a) contacting the sample containing genetic material with a lysis mixture under conditions and for a time to produce a lysate, wherein the lysis mixture comprises: proteinase K or an enzymatically active mutant or variant thereof, and a surfactant that substantially lacks fluorescence between 300 nm and 750 nm when in use for in situ analysis of DNA or RNA or a surrogate thereof, and wherein when in use for in situ analysis of RNA or a surrogate thereof the lysis mixture is substantially free of a cation chelator and additionally comprises a polypeptide having deoxyribonuclease activity, and proteinase K or an enzymatically active mutant or variant thereof, and a surfactant that substantially lacks fluorescence between 300 nm and 750 nm when in use for in situ analysis of DNA or RNA or a surrogate thereof, and wherein when in use for in situ analysis of RNA or a surrogate thereof the lysis mixture is substantially free of a cation chelator and additionally comprises a polypeptide having deoxyribonuclease activity, and b) admixing the lysate with a stop mixture at substantially the same temperature as the contacting step a) to form a stopped mixture, wherein the stop mixture comprises: at least one alkoxysuccinyl-peptidyl-haloalkyl ketone wherein the peptidyl portion of the ketone comprises SEQ ID NO:5, SEQ ID NO:7 or SEQ ID NO:9; wherein the halo of haloalkyl is mono- or di- chloro, bromo, or iodo and the alkyl of haloalkyl or alkoxy is C 1 -C 3 alkyl, wherein the peptidyl portion of the at least one alkoxysuccinyl-peptidyl-haloalkyl ketone is a tetrapeptide or a pentapeptide. and when in use for in situ analysis of RNA or a surrogate thereof additionally a cation chelator effective to inactivate the polypeptide having deoxyribonuclease activity, and wherein the stopped mixture is thereby prepared for in situ analysis of DNA or RNA or a surrogate thereof. at least one alkoxysuccinyl-peptidyl-haloalkyl ketone wherein the peptidyl portion of the ketone comprises SEQ ID NO:5, SEQ ID NO:7 or SEQ ID NO:9; wherein the halo of haloalkyl is mono- or di- chloro, bromo, or iodo and the alkyl of haloalkyl or alkoxy is C 1 -C 3 alkyl, wherein the peptidyl portion of the at least one alkoxysuccinyl-peptidyl-haloalkyl ketone is a tetrapeptide or a pentapeptide. and when in use for in situ analysis of RNA or a surrogate thereof additionally a cation chelator effective to inactivate the polypeptide having deoxyribonuclease activity, and wherein the stopped mixture is thereby prepared for in situ analysis of DNA or RNA or a surrogate thereof.